All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His Slave and Messenger.
It appears, Allah knows best, that your obligation is to obey your parents and refrain from feeding the cats in the mentioned area. This is because preventing you from doing so serves an apparent interest, which is maintaining the cleanliness of that backyard. You can explore alternative ways to feed the cats without disobeying your parents, such as placing their food in another location outside the house, like garbage collection areas or similar places.
Allah knows best.