Lightly score the covering with a hobby knife (avoid cutting into the wood)and it will peel back. Don't take off any more than you need to.
after the repair you should be able to iron the covering back down. Seal around the edges of the cut with clear fingernail polish.
There is a time (I think late August) where if you get your AMA membership it will be good for next year also.
From a financial stanpoint it may be better to wait until you can get an instructor and just stay on the SIM for now. AMA could cost less than crash damage to your airplane.
No matter what you do best of luck to you.