Feral, sick cat needs pickup

Hi all, staying with my grandma right now and she has a ton of feral cats on her property that she feeds.

One of them yesterday looked very ill — Paralyzed from the waist down and has incontinence issues. Now the issue is that idk if it has a disease, or just fell really far. It could pass these diseases to another animal or us if we try and catch it. Regardless, it needs to be put down.

Houston animal control wont pick up. Is there a service I can call?