According to my local homebrew store, you need not worry. Some people prefer to put some vinyl tile on the inside but it's not necessary. Some people also do Plexiglas, but that's a pain in the ass to cut.
Much like cincybrewer, I bent my freezer down last night. Slow and steady wins the race, and there isn't much more advice than that aside from making sure the fridge has been off for quite some time so the tubing is more pliable. Consistent moderate downward pressure should do the trick, best of luck.