"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!