There are all sorts of issues mixed together in an issue like this. Max Baer, Jr. played the character of Jethro, but he didn't create or own it. No doubt he's licensed Jethro from CBS or whoever owns "him," and these other promoters have too. If Baer has an exclusive deal to use the Jethro character, he would have a solid case.
Anyone remember a dust-up in the late 70's or early 80's between Clayton Moore, "The Lone Ranger," and the Wrather Corporation who then owned that character? They prevented him from appearing in public wearing the Ranger's mask, so until the case was settled, he made his appearances wearing wrap-around black sunglasses. With public opinion much in his favor, Mr. Moore eventually won out.
I was acquainted with the late "Irish" McCalla, the pin-up model who played "Sheena of the Jungle" on 1950's TV. On the advice of her friends Bill Williams and Barbara Hale, she demanded her personal-appearance rights in her contract. According to Irish, that was how she made a living and raised her sons after the show ran its course. She did in fact try to buy the Sheena character and continue producing the shows herself (Dick Powell's Four Star TV company was ready to back her) but could get nowhere. McCalla Enterprises, the company she and her sister created at that time, was later revived to manage her second career as an artist and illustrator. Irish was a naturally gifted painter, self-taught, and worked in an "Americana" style comparable to Norman Rockwell.
Max Baer was smart in moving to the production side of the business, because as with Moore and McCalla, he was hopelessly typecast with the public. I've seen some pretty pathetic examples of ex-stars on the downside shilling for some dodgy schemes. I especially remember Burt Ward (Batman's "Robin") doing a late night infomercial offering a Bell & Howell movie projector and a package of 16mm prints of those 70's grizzly-bear-and-old-trapper movies as a "business opportunity" for something like 12 grand. The idea was to make BIG BUCKS showing the movies in church basements. (Wonder who bit on that one?)