It probably depends on your mother's mental state and whether she agreed with your sister (being of sound mind when she did so) that the house could be let. If she did not agree or was not of sound mind then - in the absence of a power of attorney - I don't see what authority your sister has to let the house. (This assumes it is owned solely by your mother.)
What would she do if your mother's health improves and she want to return home?
If she has used her own name as landlord on the tenancy agreement it might even be that the agreement is voidable as she had no legal right to enter into it.
However, I have no idea what you can do about it - you would probably need to consult a solicitor & this could be costly.
Incidentally, if she does get power of attorney she should keep quite separate accounts of all income & expenditure made on your mother's behalf so that she can account for it properly if questioned.