If I were to delete Outwitters on my phone, but play on my iPod, would that mess with anything? Or could I continue on like normal?
If you have the same GC account on both and restored your purchases on whatever one you didn't buy them on (assuming you bought teams/bases), nothing will be affected and you can continue your games like normal.
Just make sure you didn't start any turns on your phone because it will lock you out of your matches on your iPod. Either finish all of the turns before you switch or never start them at all.