1. You can upload the map with the only difficulty that uses the background you want.
To do that, go to File --> Open Song Folder. You can see several .osu files depending on how many diffs you have in the set.
Use the difficulty name in the square brackets at the file name to determine which one you have to move temporarily to somewhere before putting it back after uploading.
2. With the above one in mind, that also means you can change it on your own will.
After that however if you want to change the one in-game for you (and for others as well) go to Options --> Open osu! folder, then go to Data --> bt (Data folder is hidden btw).
Look up your map ID on the web URL (the number after /beatmapsets/ and before another number) and then find it in the folder. Once you found it, delete the image and refresh the game.