Personally I haven’t had any problem removing badges but if you’re trying to remove your badges and find they are being replaced by Steam SquidLordWilliams explains how to prevent Steam from replacing them here:
Finally! A method to DELETE files stored in Steam Cloud servers!
There’s a certain tricky bit in that HWR doesn’t use the S2 file
buffer in the app-number specific directory (as they refer to it,
“/remote”) but just roots itself in the S1 / “profiles:” directory.
So, the short version of the trick is to note that to force the Sync Conflict, Steam needs to be exited, you need to actively change the content of any/all of the TGA files in “profiles:/badges” (I did so by simply saving a flipped version of a badge to all of the files in there via PhotoShop – it was convenient), and then starting Steam, then HWR, which gave me the Sync Conflict pop-up, and before going any further with the pop-up, leaving it open to the side, deleting the “profiles/badges” directly entirely. Tell Steam to upload a new Cloud Sync from disk and whoosh, it synchronizes to only what you have on disk.
Don’t ask how long it took to get that process figured out.
But this works.