Does riding high gear up a hill damage a recumbent bike? I have a recumbent trike with 26 gears. While normally I would shift to a low gear when going up a hill, I found that I can go up hills in the highest gear, the configuration that gives me the fastest speed on a flat. This may be because the bike relies on pressure between the seat and pedals instead of pressure from gravity, so I can put more force into the pedals.

Does riding a bike in high gear up a hill put unusual stress on the parts? It does not have high-end parts. E.g. the front and back derailleurs cost $75 together and many of the other parts can be found at Walmart. Does riding up a hill in high gear put too much pressure on a bike that the bike's parts are not designed to handle?
The bike will be fine -- the riding conditions are within the specifications of the bike components.

The bigger issue is you -- you don't want to end up damaging joints and what not by overexerting yourself.