I don’t remember him being think-skinned about it.
It was a thing at one time. Madden used to do a segment on KCBS radio in the Bay Area, and I was listening one day when one of the on-air personalities mentioned something about the Caliendo impression and Madden’s normal jovial on-air personality completely changed and he made some comment along the lines that he guessed that the guy (Caliendo) did what he did to make a living but it was a dishonorable way to treat people.
Charles Barkley isn’t necessarily the most reliable witness but in this case I believe him, as I detected genuine bitterness in that radio interview I heard.
“Charles Barkley Reveals that John Madden Tried to Sue Frank Caliendo Over His Madden Impression”
https://www.cracked.com/article_38076_charles-barkley-reveals-that-john-madden-tried-to-sue-frank-caliendo-over-his-madden-impression.html