Hi! I know this doesn't help much, but just to confirm what you might have already guessed, as far as I know since bitsy game data is stored on your local browser, if it's been deleted and is not available in local storage anymore, then I don't know that you can retrieve it.
I hope they didn't lose too much work, or that someone else is able to speak up with a retrieval solution if one exists.
Also fwiw, I appear to have my uBlock Origin turned off for the bitsy page, so I must have had compatibility issues with it at some point in the past. I think you are right that that may be the source of the issue. Have them try turning it off for bitsy and seeing if that fixes the problem.