I know, that Homebrew doesn't upgrade casks with auto-update (without force). So eventually, software versions, actually installed, and tracked by Homebrew, become different. For example:
$ brew cask outdated --greedy
firefox (79.0) != 80.0
google-chrome (84.0.4147.105) != 85.0.4183.83
microsoft-edge (84.0.522.48) != 85.0.564.41
Firefox, Chrome and Edge auto-updates themselves and actually has latest versions. But Homebrew doesn't know about it.
So, is there a way to tell Homebrew, that some cask is the latest version already, without reinstalling cask with brew? Just update record in Homebrew database (or whatever brew stores casks' versions in).