Please help: I uninstalled a mod named "Bitter Island" which conflicts with the mod "Juniper's Twin Lamps", but for some reason it doesn't disappear from the world map. When I use the "Update map" function in Wrye Mash, it does disappear, but the whole map becomes messed up: it gets covered with perpendicular lines dividing it in squares, there are strange visual glitches on parts marking the explored areas, the island from the mod "Riler-Mosh" disappears from the map (even though not uninstalled and I can still get there), and a part of Tamriel Rebuilt is cut off.

Is there any way to get this Bitter Island off the map without ruining the rest of it?

You could try deleting the FMAP record by Enchanted Editor which will allow the game to reset the map completely.

You can turn off the gridlines by disabling the World Map Gridlines feature. (under your Saves tab, right click on the File header)

But the visual glitches can't be fixed. It's always a bad idea to update your map mid-game, as the game seems to get confused about what/how to display the info from your save file.

edit: what Envy suggest might work