IPA: //ˌkaʊntərpəˈtɪʃən//
KK: /ˈkaʊntərpɪˌtɪʃən/
A petition that is created to oppose or respond to another petition.
The community submitted a counterpetition to challenge the original proposal.
Counterpetition is formed from "counter-" (meaning against) and "petition" (from Latin "petitio", meaning a request or appeal). The word refers to a request made in opposition to another request, typically in a legal context.
Think of making a request that is 'against' another request — 'counter-' means against, and 'petition' means a request.