Officially it should be one months notice, so you could make a claim with for a weeks rent from the deposit. If it were me and they had been your tenant for a significant period of time and they had been a good tenant, I would let it go and wish them all the best.
Unless your tenancy agreement allows for less notice, the tenants notice is invalid. It should be a min of a month expiring at the end of a tenancy period. The tenancy periods are usually but not necessarily the same as rent days.
You are free to accept an invalid notice or you can ask the tenant to serve a valid one. If you decide to accept, do it in writing.
I would recommend that if they have been a good tenant or they are one you would like to see the back of, accept the 3 week notice in writing and move on.
I agree to some extent but if the tables were turned , would the tenants do the same .
I think to be fair they should honour the contract as they will go through life cheating the system.