It still maybe not be legal under Spanish law,. That each party has signed does not make it so.
I believe it should be signed in front of a Notary and it miust be register (I think with the local authority?).
Most rentals don't do that as of course then the tax on the income cannot be evaded, and maybe IVA too as an agent is used, as is mostly the case.
Nevertheless, I suggest as I said;
a letter from the owner and a copy of her DNI and a copy of the escritura would do it.
And, If all else fails DEMAND the complaints form and complete it.