Exactly. If you want good advice, listen to Mr P.

The phrase "does not invite" is a present tense (simple aspect)

The phrase "has not invited" is also a present tense (perfective aspect) . The present perfect is not a past tense.

Most of the problems which learners ( and even some teachers) have with the present perfect stem from the mistaken belief that it is a past tense.  The clue is in the name, surely? Present perfect?

The key thing to remember is that this verb form connects the past with the present, and it always gives us information about the situation now.

Past tenses tell us about the past.  Present tenses ( including present perfect simple and present perfect continuous) tell us about the present.

In this example, the present perfect tells us that the writer is currently still waiting for an invitation to someone's new house.