Inspector Jaime Peña planted evidence (the invoice) with the papers that the police got from Gloria Villaverde (Mayka Villaverde's sister and lawyer). This is to make it appear that Mayka hired Javier Alonso (the private detective) to follow and investigate Alex Ulloa. From the dialogue of Peña to Ulloa:
The detective... was a bargain.
I just had to put the invoice in the dossier.
Eva and I took care of the rest.
Javier Alonso is conveniently on a trip.
And of course, he didn't find out anything.
The only thing on record is that Mayka hired him.
The whole thing about Javier Alonso finding out about Ulloa and Carla Miller's affair was made up by Peña and his daughter, Eva. It is likely therefore that Mayka was telling the truth that the person she met in the restaurant was her psychoanalyst.