A team member created a quickfilter with an invalid JQL statement, and didn't notice the cross showing it was invalid, and added it anyway. After doing this, removing/deleting the quickfilter doesn't work in most cases. The invalid JQL statement was "labels = SRP-*" for example.

Clicking the 'remove' button on this quick filter came up with a confirmation dialog and the option to delete. After clicking delete it was still there.

Changing the query to a valid JQL statement did not work either. The query stayed the same after clicking 'Update.

Workaround:
I managed to delete it purely by accident, by changing the query to just a new line character, clicking update, then deleting. However it took me a while to figure that out. Even changing the query to something valid didn't seem to work.