Old gunsmith advice - if your driver bit does not apply torque to the screw primarily at the bottom of the slot it will chew up the top of the slot or worse. Many times it is necessary to slightly grind the bit so it grabs the slot at the bottom and not at the top. This applies to slotted, philips, Allen and Torx fasteners. You would think all of the screw and bit manufacturers would be working off the same blueprint - but they're not. The other issue here is that most of these screws are sub-sub contracted from some place in Taiwan and they're made from recycled tuna cans. They strip out as fast as you can replace them. On an Allen or a Torx the bottom of the driving slot is punched down below the head into the threaded shank of the screw so there is very little metal around it. Do not over torque those types of screws or use thread locking compound or the head will shear off. Then you'll have a real problem. Torx screws are the work of the Devil. I hate them.
OOOOOOOH . . . almost.
I was going along there thumbs up and YEAH brother . . . until the last line :
Torx screws are the work of the Devil. I hate them.
Nah dude, nah.
They have way more purchase on the interface between tool tip and fastener. Total perfect design. Want to talk crap / work of the Devil think Phillips screw. The bit kicks out just about the time one is about to get it tight enough or about the time it is going to loosen the fastener. The only reason for Phillips is it is self aligning and easy for automatic assembly machines and drywallers to geeeeeeter done.
Can we agree to say : Poorly made "sub-sub contracted . . . in junk metal" and not heat treated (most of the fasteners in the knives we see) are the work of the devil ?
Nah, good quality Torx are a god send even over Allen / hex socket screws.

As far as the original question :
When is a screw classified as damaged
I can't add anything constructive except to say : When it is in one of our pocket knives.
Most of the fasteners I see in pocket knives are already more damaged than yours right from the factory and are so soft they are iffy to fool around with especially the ones where the misguided fools at the factory over did it with the locktite. I have never had one shear off in a pocket knife but don't doubt it will happen. I have had a few round out (don't call it stripped; that bugs me. Stripped is when the threads shear off in the business end.)
I say if you find a source for REAL Torx screws (well formed out of good steel and heat treated) you will love them and I would recommend replacing all the screws in the knife with these on the first rebuild.
The case for QUALITY Torx
bits cannot be over stated as well.
And yes, for sure, do grind the tip of the tool bit as drail recommends ! ! !
It won't be as easy to get the bit into the fastener but it will SURE AS HECK get a better bite in the fastener ! ! !
