Yes they are technically liable for rent month to month, but sometimes a few extra days maybe useful to you in which case why reject it? Depends on circumstances.
If it does not affect a future tenancy then why not go for it.
Youve created a brand new tenancy. Think carefully about the implications before pursuing the tenant for this. However, it would be interesting to know why Openrent a) didn’t warn you about this and b) chose to charge a pro-rata rent.