2,3,7,8-Tetrachlorodibenzodioxin, also known as TCDD, a part of Agent Orange
Aryl hydrocarbon receptor
vertebrates have, killing them if they consumed enough.
so if your humans really want to wipe out all wild vertebrates, they just have to spray everything with tons of TCDD, killing all vertebrates on land, and then pour it into the oceans, killing all vertebrates there.
it is solid, you have to solve it in something else (chloroform) to be able to spray it properly. but because it is not a gas, it is easy to keep citys save. (of course you have to kill rats etc per hand)
so humanity could kill all non domesticated vertebrates.
but earth stays liveable after that since some crops sustain TCDD.