Have I damaged my tyres? I noticed after mounting some new tyres that part of the side wall, just above the bead, seems to have been damaged while I was fitting them (see photos below).

These tyres were especially difficult to mount, even with the bead seated in the rim's bead well all the way around.  So tight, in fact, that the only way to get the bead out of the well and seated under the bead hook was to pump it up to a much higher pressure than I would ride it with and wait for it to "ping" into place.

I think it's this process that ended up causing the damage you can see in the photos.  The tyres in question are these (folding version).

Have I compromised my tyres, or should I not worry about it?
Those strings are quite common with continental tires and seem to be a part of their manufacturing process. Every continental tire I have owned seem to have some of those threads, even ones that mounted relatively easily. I just cut them off and have never had an issue with them. Continental tires are also well known for their tight beads.

The high-pressure technique is a common technique to get a bead to seat. To speed it up you can also put the tire in a vice and pull on the top of the wheel to try and force the bead to seat.

As an aside, many recommend against running fenders with  knobby tires, as the knobs can pick up debris (e.g., small sticks) that can jam in the fenders causing a crash.