Given that Bo-Katan made no move to claim the saber afterwards— she literally piles it with the rest of his stuff after rescuing him and doesn’t make any comment whatsoever about it — she clearly disagrees. Oh, she knows she could easily defeat him in any actual duel for it, she’s a vastly more skilled fighter, but a huge part of her current character is the whole depressed, demoralized slump she’s in.Dinn lost the Saber in combat. He was literally bested. He can't just say mine again when he is literally rescued by Bo wielding the Saber. If other Mandos had seen the fight. Would they have wanted Dinn to remain Mandalore if he lost a fight in such a manner? I think not.
(For that matter, she damn well knew she could have taken it from him at the end of Season 2 finale; it’s just that she apparently felt that challenging him on the spot would have been dishonorable under the circumstances.)