Caustic oven cleaner that contains lye will take the paint off.
Use appropriate protective gear for your eyes, skin and clothing. Old-school lye paste would be best, but if all you can find is the aerosol type, use it when there is no wind. You don't want to be breathing the mist.
Use enough oven cleaner to wet the paint surface and keep it moist for at least 30 minutes by misting with a pump spray bottle with plain water. Keep wild birds, pets and children away. Do not leave the lye patch unattended.
After about 30 minutes, use a stiff bristle brush on the end of a long pole to scrub the paint slowly. You don't want to be spattering and splashing lye all over the place. You should see the paint transform into tiny specks or flecks instead of a solid sheet. The flecks will wash away with water.
When you think you've done all you can with the brush, flood with lots of water using an open hose-end, not a nozzle. Avoid splashing. Continue scrubbing with the brush and a flood of water until all traces of lye have been washed away. You can test for completeness of rinsing by touching the surface with a bare finger and rubbing the wetness between your thumb and finger. If it feels slippery like soap, you're not finished rinsing.
Grass won't be harmed by the runoff as long as you dilute with plenty of water.
I've done this methodology on concrete by making my own lye paste from lye flakes, water and corn starch. It worked great and didn't harm the concrete. It looks like your surface is blacktop, so proceed at your own risk, and perhaps try a small patch before you go full bore.