The months notice is a full rental period not a calendar month
So technically she leaves not next month on the 22nd but the month after, June 22nd
Speak to her and see what you want to do
As above, her notice is invalid, but if you are happy to accept it plus 6 days rent, then you should reply accepting the notice and stating this. Without your acceptance, the tenancy won’t necessarily end.
You could point out that the contract “officially” ends on X date, but you’re willing to let it end sooner if they are willing for you to arrange viewings before they leave - this way you get it re-let sooner and there’s less of a void when the tenant leaves. Of course this is subject to the usual Covid nonsense at the moment…
Why is the notice a full rental period and not a months notice from the date of serving? Surely it depends what is written in the contract and we haven’t been told that in the original post?
The default position, (common law notice to quit) is a minimum of a month expiring at the end of a tenancy period. Most tenancy agreements are based on precedents drafted by solicitors that are going to say the same thing. You are right that it’s possible that the OP’s contract over-rides this by giving a bare month, but it would be extremely unusual.