Term for an insincere invitation..?

Solution 1:

You could call that a pro forma invitation.

pro for·ma
adj.
1. Done as a formality; perfunctory.

In fact, perfunctory itself would serve:

per·func·to·ry
adj.
1. Done routinely and with little interest or care: The operator answered the phone with a perfunctory greeting.
2. Acting with indifference; showing little interest or care.

If it were required that you invite someone even though you might not want to, you might label it an obligatory invitation.

But there are no long-standing words I know of that pertain only to invitations (such as your faux-vite).

Solution 2:

I've heard this called an "unvite," but maybe that was just on Seinfeld.

Solution 3:

They could be described as as token or nominal invitations. Either would suggest that only the most basic socially acceptable gesture has been extended to the recipients.

Solution 4:

A "courtesy invitation" is extended when you don't really expect it to be accepted.