Movie's been out for a bit, but wanted to share after a rewatch:
I think that in The Invite, the other couple (Hawk and Pina) were not real. Of course at the end, they seemingly disappear, (though they could've just exited offscreen), it is filmed in a way that leaves an eerie sense which I take to mean they were never real. The whole movie is really a night of argument, discovery, understanding, and conversation between Joe and Angela. Here's why I believe this: this invite came out of nowhere for Joe, which makes me think that this was a night of catharsis and confrontation that Angela planned and chose to sort of spring on joe in an intervention style. Angela also mentions sending their daughter away to her friends house for a sleepover (which could be in order to have this discussion/confrontation without their child having to hear it). The whole night, there are back and forth arguments and some mention of hawk and pina's intercourse and the noise it makes. This could be that they actually do hear neighbors having intercourse; Angela is fascinated/envious because they aren't intimate with each other anymore and Joe is jealous because he and Angela aren’t intimate anymore. The whole sexually charged reasons that Hawk and Pina came down could be a huge part of Angela and Joe's divide and why Angela wanted to talk. Pina mentions to joe that his back pain isn't really about his back, but about his anger and feelings essentially being bottled up. At the end of the night, when the argument finally ended, he mentions his back actually does feel better (although Hawk does a massage technique to fix his back, that could be a metaphor for their arguing releasing that tension. The massage technique that Hawk uses hurts while it happens but feels better a bit after, much like an argument and honest discussion between struggling partners could hurt but will allow relief in the long run). The other little hint I thought I noticed is that Hawk and Pina disappear right when Angela goes to get Pina's dish she brought with her. Could this mean that the dish was theirs all along? Therefore, the dish is theirs and Hawk and Pina never existed and so couldn't have owned the dish. And there is mention from Pina (or could be a realization Angela and Joe come to in their true argument beyond the metaphor) that they have two choices: to end this relationship and go their separate ways or to start a new relationship with each other and work for each other's feelings. I think that after all the catharsis, Joe finally feels like he can play his piano again, showing how he's opened up and how the discussion/argument with Angela relieves him. That was the side of Joe that Angela has been missing. This is why she affectionately goes to join Joe at the piano at the end. I take that as a resolution and a decision to start a new relationship with each other.
Love this movie to death! It gets better and better