"Invite" is a transitive verb, so it MUST have an object after it. Thanks for inviting. = WRONG Thanks for inviting ME. = RIGHT You can also change "invite" to a noun (invitation). Because it is a noun, not a verb, you are not required to put an object after it. Thanks for your INVITATION. = RIGHT So "Thanks for your inviting" is not correct. "Thanks for your ..." should be followed by a noun. (Thanks for your invitation.) And "inviting" is a verb in -ing form so it should be followed by an object. I hope that helps!

It makes sense in a crude way, but you would never hear a native speaker say that.

Thanks for inviting me

Like mattmorich0 said, a "crude" way. I like that, "crude". So you can say "thanks for your invite", though, in a slang way.

Thanks for inviting Thank you for your invitation.