"So," says Loki. "Odin can get the short version of that story and decide whether she wants to re-banish me or announce that Tesseract-based magic is just as special as eye-sacrifice-based magic or what, and if it's the latter I want to bring a bunch of people here to look around."
"Well, that you can do either way, I can bring you to them without having to set foot on any planets Odin might care to banish me from, but they'd still like to see the place."
"It wouldn't be right to banish you!" says Thor. "I mean - you did use magic in battle, sort of, but - but I cannot believe there was any dishonour in saving the people of Arda."
"You know what's really fun? Sparring when both people can teleport. It's great."
Thor giggles uncertainly and shakes her head. "I hardly know what to do with you, sister."
"Well. I'm glad you have taken the sorcery and my inconsistent color scheme so well. I worried."
"...I thought you were dead, these past twenty years. I mourned. I don't - I don't know what it can possibly mean, that you're - but you're my sister, and I love you, and that's all I need know."
And when Frigg and Thor have gone (Frigg to explain things to Odin, Thor to back him up and be indignant about the possibility that her sister could be rebanished or anything of the kind), Loki turns very seriously to Sigyn and says, "Something I did not choose to emphasize in that rendition of my adventure is that oh stars it has been subjective decades since I got laid."
"Is my room a depressing memorial site or what, do you still live in the same house...?"
And now they are in his house and now they are not wearing clothes it has been too damn long.
He is very glad she thinks so! He thinks the same of her. Look how much he appreciates her life and presence.
And after... Odin has had some time to mull it over... Loki goes back to the palace again, checks out her room, swaps her pitted armor for a spare set.
And goes looking for her mother.