This quest is a quest that would not normally be assigned. The reason this quest popped up for you after playing online is that whoever hosted the game had modded their save file to make them have that quest, and because you joined them, it was passed on to you. There is no way to complete it in game, so you'll have to use WillowTree (a Borderlands modding tool) to mark the quest as completed.
Download it from that link, unzip it, and run the exe. Click the willow tree icon in the top left and select Open. Go to your saved games (Documents/My Games/Borderlands/savedata) and select the right save. If you don't know which one it is, no worries, just open one of them and go to the General Info tab in WillowTree to see if that's the right one.
Once you've opened the right save, go to the Quests tab, expand Playthrough 2 Quests, and select Keeping Your Insides Inside. Open the Progress dropdown, and select Finished. Then click the WillowTree icon again, hit save, and load up your character in game. You should no longer have to worry about trying to finish that quest.