There are several things that are confusing about this lesson - the terms and meanings. You use both pretérito perfecto (once)

Question

and pretérito perfecto compuesto (twice) in the same lesson for the same verb form. Is it possible to use just one. 
Also, in my experience, ha invitado has usually been translated as has invited rather than invited/ ha visto as has seen rather than saw.   So, I would then translate había visto as had seen. This is very confusing.  Help. K

Answer

Hi K,
Inside the lesson the term used for this tense is El Pretérito Perfecto. It is when you click on the link for a wider explanation of this tense where you find the other terms. The reason why we use all possible terms is because there are students who have been taught this is the Pretérito Perfecto, others that learn it as the Pretérito Perfecto Compuesto, and in Latin América they usually learn it as the Antepresente. We decided to use in the lessons the term that we think is more widely used, but give the other terms alongside to clarify.
In reference to your other question, this tense in Spanish generally translates  into the simple past in English (I did, I went, I saw..). That's why you will often see phrases like "He visto" translated into "I saw" and not "I have seen". But in lessons that test conjugation you will always find what tense to conjugate in the hint, to clarify.
Sorry it is a bit confusing.
I hope this explanation helps a bit.
Inma