From examples I found, it’s not usually that periodic, but some mantis species make a very scratchy sound when threatened, sometimes repeatedly, but at more irregular intervals.

My yard is full of praying mantises, but they are usually dead quiet, I’ve never heard one make a noise (I try not to bother them). It’s definitely not a common trope sound like crickets… I was hoping there was some nature documentary that aired in the early 80s that featured a mantis sound that Larson might have seen, that could have inspired this cartoon idea, but so far can’t find a specific one. There was an episode of Life on Earth from 1979 (presented by David Attenborough of course) about insects that featured some mantis stuff, and lots of insect sounds in the background, but not a specific mantis sound (they seem to play a cricket sound during the mantis scene in the background)

There was also a song “Praying Mantis” released in 1985 by Don Dixon that featured praying mantises in the video, but can’t connect that one of the strip either :)

I suppose it’s also possible that is supposed to be a cricket rather than a mantis… or that Larson didn’t really differentiate between them or their sounds, and it might have been as broad as “insect interested in insect sounds”

Edit: I had an alternate thought - maybe the mantis wants to eat a cricket ! :) But then the connection to his master’s voice is weakened… oh well, dissecting jokes really does kill them…