You shouldn't erase the stick. In this case your savegames will be lost.
I'm sure that your xBox don't recognize the stick as it was removed while it's in use. Many file systems have a marker in it to display if a stick was previously in use.
You can reset these markers by removing them properly. In your case, your xBox is the only thing which can read it, I would recommend to try the stick on a linux and remove the stick savely. Normally it should reset the flag. As far as I see, it is a kind of FAT32 file system which is used, you can try to load it on your windows PC and remove it savely. Be sure you won't format it, if your windows will ask you for this.
After that try it again on your xbox.
By the way, if your not sure what your doing, you can take a complete image of the raw usb-image as a backup to restore it if you fail. If your not so experienced, ask a friend which has good computer knowledge to do it for you.