MacBook Pro 13" late 2013 battery swelling

So I recently bought a used MacBook Pro. I knew it wasn't going to be in great shape (it's not my main computer) but unfortunately it came with the "Condition: Replace soon" message for the battery. The battery life itself is still very usable, but the bottom panel of the 'book has mild swelling; it is most obvious when I try to lay it flat and it rocks around on the swelled part on the bottom. So, my question is, what is the most expedient way to fix this? Ifixit has a diy replacement kit that seems good. My question would be, if I replaced the battery myself, would I be able to fix the aluminum panel by straightening it out with a hammer or something?

Apple can fix the battery themselves (at cost, of course) but would they also fix the swelled panel or replace it if I sent it to them for repair? What do you think would be the cost of a full repair (battery and panel), roughly speaking?

Specs:

13", late 2013

2.6GHz i5

8GB ram

121GB SSD (Might not be the original SSD)

Let me know if you need more info. Thanks for any help!