Here's my predicament : by mistake I made 'Timeshift' write its snapshots on my main HD. Realizing the blunder, I did stop the backup, but there's still a folder on my drive called /timeshift/snapshots, which is more than 37Go large.
The obvious solution would be to just move the folder with the snapshots to another drive, then change the Timeshift settings to backup to the proper location. There's nothing special about it, it's just a big folder.