In the FAQ for this site, peeving about grammar disguised as a question is discouraged. The various forms of peeve in Merriam-Webster however does not justify this usage.
Peeve is a verb meaning annoy, forming peeved and peeving. It is also a noun meaning grievance. Peevish is an adjective meaning ill-tempered.
Peeving about grammar then would suggest one can rewrite the phrase as annoying about grammar which does not make sense. How common then is this usage of peeving and is it legitimate?