I believe you could use suction pad with diameter smaller than size of light bulb.
GU10 lightbulbs are usually flat
so suction pad can easly adhere to this ligthbulb.
Then you could catch suction pad to unscrew lightbulb.
I think one of these could be used as they have screws attached so it might be easier to catch with some tool.
lifehacks.stackexchange.com/users/9461/running.t
I have this exact problem with one of my light fittings.
When I bought the light, it came supplied with a special sucker for removing and refitting the bulbs.
Stupidly, I used the device when the bulb was hot - and melted the soft rubber.
What I now do is to use disposable latex gloves, pushing the front glass quite firmly with the extra grip of the thumbs is enough to turn the bulb for removal and refitting.
If you have normal household rubber gloves, this will probably work even better, but I just happen to have latex ones and none of the others.
Be aware , some (cheaper) GU10s have a very thin piece of glass with a square edge that is bonded to the front of the bulb.
This square edge is razor sharp and will slice your thumb open without the gloves.
Even with the gloves it is possible to cut yourself.
Know your enemy!
Extra tip - when you replace the bulbs next time, get really high quality LED bulbs.
Not only will you get all of the standard benefits of LED bulbs, but they will last for around 7 years so you will minimise the number of times you need to change them in the future.
lifehacks.stackexchange.com/users/1965/Lefty
A piece of flexible plastic tubing that just fits over the bulb makes a handle.
This is also helpful in changing bulbs with broken glass.
If you can't find a tube of the right size, tape some plastic sheet together to make a tube, or better, a slight cone, so that it slips over the bulb and grips tightly.
Gentle warming makes the plastic stick to the glass better.
A plastic soda bottle may also work:
lifehacks.stackexchange.com/users/2012/DrMoishe Pippik
I always got one of these when I bought a fixture - link to ebay GU10 tool its an answer to your stated problem however since it comes with a fixture when bought new, its not really a lifehack as such edit: this is better as you get leverage link to amazon tool with a handle
lifehacks.stackexchange.com/users/18058/bigbadmouse
If you can put some adhesive tape in the 3-4mm space, and press it against the side of the bulb (maybe with a paper clip, tooth pick, spatula, or some other slim implement), you may be able to pull the bulb out of the socket with the tape.
I would do 2 pieces of tape, with the first one opposite the second one (180 degrees away).
lifehacks.stackexchange.com/users/4198/BrettFromLA
What i found works is get a plastic bag and cover the light get a par of pliers or channel locks.
Brake the glass covering the bulb( wear safety goggles then grab the light with pliers or channel locks just enough to grip ( try not to break the bulb ) and twist counter clockwise should come out.
lifehacks.stackexchange.com/users/30379/Tremendousdennis
Based on pictures (not having actually seen these bulbs), I would get a small piece of wood, perhaps 3 cm on a side, then coat the top in hot glue.
I would press it up against the bulb until it bonds.
Wait ten minutes.
Then unscrew the wood.
Tips:
Standard hot glue (EVA) is mostly debonded with alcohol (IPA or ethyl).
A spray bottle of rubbing alcohol can help you get the wood block off it
it was stuck wrong.
If the bulb is inset deeper than the ceiling, use enough hot glue to fill the gap, or use a smaller piece of wood or wood shaped like the bulb (so it can stick without the ceiling blocking it).
lifehacks.stackexchange.com/users/4092/piojo
I am trying to remove GU10 lightbulbs from a light fixture.  The fixture makes it very difficult to grip the edges of each bulb (only about 3-4mm clearance).  Is there a lifehack to remove GU10 lightbulbs from such fixtures?
Lifehack to remove GU10 lightbulbs from light fixture?
lifehacks.stackexchange.com
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lifehacks.stackexchange.com/questions/17802
lifehacks.stackexchange.com/users/9463/RockPaperLz- Mask it or Casket
There are a number of different ways of potentially removing a GU10 lightbulb, and one simply way would be to use a suction pad or a special GU10 remover tool. Alternatively, you could wear some rubber gloves and press against the glass to get friction or cover the bulb with a plastic bag and use some pliers. Another way of remove them would be to glue a piece of wood to the glass and then simply unscrew it. The options are to try a suction pad, rubber gloves, a piece of tubing, a GU10 tools, sticky tape, pliers or a piece of wood glued on.
There are a number of different ways of potentially removing a GU10 lightbulb, and one simply way would be to use a suction pad or a special GU10 remover tool. Alternatively, you could wear some rubber gloves and press against the glass to get friction or cover the bulb with a plastic bag and use some pliers. Another way of remove them would be to glue a piece of wood to the glass and then simply unscrew it. You could use  suction pad  with diameter smaller than size of light bulb or  use disposable latex gloves, pushing the front glass quite firmly with the extra grip of the thumbs is enough to turn the bulb for removal and refitting. A piece of flexible plastic tubing that  just  fits over the bulb makes a good handle you could use.  If you can put some adhesive tape in the 3-4mm space, and press it against the side of the bulb (maybe with a paper clip, tooth pick, spatula, or some other slim implement), you may be able to pull the bulb out of the socket with the tape.  
Disposable latex gloves provide extra grip to push the front glass firmly when removing GU10 bulbs. A small suction pad, a piece of flexible tubing or adhesive tape have also been recommended. There are a range of options available, including using a suction pad, latex gloves, adhesive tape or flexible plastic tubing to pull the bulb out of its socket.
Know your enemy!
Know your enemy!
Try a suction pad. Use rubber gloves. Fit a piece of tubing over the bulb and twist. Use a GU10 tool to lever it out. Attach sticky tape and twist. Break the glass cover and grip with pliers to remove. Glue a piece of wood to the bulb and twist.
You could use  suction pad  with diameter smaller than size of light bulb.   You can use disposable latex gloves, pushing the front glass quite firmly with the extra grip of the thumbs is enough to turn the bulb for removal and refitting. A piece of flexible plastic tubing that  just  fits over the bulb makes a handle.  If you can put some adhesive tape in the 3-4mm space, and press it against the side of the bulb (maybe with a paper clip, tooth pick, spatula, or some other slim implement), you may be able to pull the bulb out of the socket with the tape.  
There are a range of options available, including using a suction pad, latex gloves, adhesive tape or flexible plastic tubing to pull the bulb out of its socket.