No, Josh, there are other options besides ripping down the drywall you have installed, but that may be the easiest and cheapest solution.
Best solution: Install Kerdi over the drywall and seal it to the tub with Kerdi-fix. Bulletproof installation. Kinda expensive, though.
Second best solution: Remove the drywall compound and tape, tape and mud the joints with thinset and CBU tape, then coat the walls with 2 coats of Redgard or other liquid waterproofing membrane. Caulk the joint between the drywall and tub before setting the tile. Note: this is not a listed method in the Tile Handbook. There are no methods for using a liquid membrane over drywall in a shower. A tub surround/shower is less stressful on the waterproofing, so as long as you are diligent with your caulk maintenance, you should get a lot of service (years) out of the tilework before it needs replacement.
Cheapest solution: Tear down the drywall, install plastic sheeting over the studs and drape it into the tub. Install backerboard. Trim the plastic flush with bottom of backerboard. Tape and mud the joints with thinset and CBU tape. Caulk the joint between backerboard and tub.