he asked loki directly, a real invite. not some fodder background characters that obviously never stood a chance from the readers point of view. Since there a gag/funny random moment that not serious.
Loki is not a background character. He also got disappointed when hajrudin said no to him for letting loki join him., When luffy said he take responsibility for loki.
Showing Luffy invite was real and not bs, since he said he watch over loki on his crew. Taking responsbility for a strong character everyone originally thought was bad/dangerous cold blooded killer. etc
Well now that loki is freed, Luffy still reminding us he taking responsibility for Loki. with saying he can kick loki ass. etc.
Luffy has not forgotten. Even Nami knows, and got annoyed when she saw luffy show up with Loki. She like oh great other one for the crew. Also Loki got upset he got scolded lol, Nami intimidation powers to every guy who joined the crew.