I can't understand what you are thinking of. The easement is in your favour - it gives you the right to connect to their drains. I assume it also includes provisions for you to share any maintenance costs. If it does, you need to do something about bringing it to an end, as otherwise you could be hit with a demand for costs at some future time. Also, you want it removed from your land registry entry.
None of this (it seems to me) means the easement has any value to the nursing home. In fact ending it might disadvantage them, as maintenance costs would no longer be shared.