Invite back
Definition 1 of 1
Pro Tip 1/3Repeated Welcome
Suggests you were a good guest and the host enjoyed your company or contribution. 
After the poetry reading, they were eager to invite me back.
Pro Tip 2/3Casual Use
Often used in casual, friendly, or social contexts rather than formal or official situations. 
The game night was a hit, so let's invite them back!
Pro Tip 3/3Future Implications
Implies a sense of looking forward to future interactions or events. 
You made a great impression on our team; we must invite you back for the next project.