Last tested: Sep 2020
"Stash" has multiple meanings with respect to Git:
It's the old name for Bitbucket. They rebranded in early 2018. Looker does support using a Bitbucket repository for Git integration.
git stashis also a Git CLI command. Basically it stores away the changes in your working directory so you can start fresh. Git docs. The same effect could be achieved by committing to a branch, and then moving to a branch that has been restored to production. Looker does not implement the stash command, and you may run into errors if you use stash on your repository while it is connected to Looker.