The quest can't be deleted because you then you could use the item over and over to endlessly farm the thing you get from killing the monster in people's houses.
The quest item can't be deleted either, so you should still have it somewhere, just complete the quest normally.
To get into the houses, you need to either go to the aven house guy, the guild town house guy, or the guy in golden plains.
Then hit search and enter anyone's home on the list.
If you are having trouble entering through one innkeeper, just try another.