Inviting people still works (sorta) on the mobile platform. One way worked and one way didn't.
(1) On first screen, I went to "COUNTRY CLUB" (left side button). Saw a button for owners tools. That got me an option to "invite friends to country club." But when I clicked that, I got a list of "unaffiliated friends" to invite that included only 4 people --- NOT including the friend who was the one I was wanting to invite. (and he's completely without a country club, so "unaffiliated" did apply).
(2) So then I went back to first screen that opens on platform. Clicked on FRIENDS (another left side button). Found the friend I wanted to invite, clicked and got that friend's profile. The button was there for "invite to country club" like it would be on non-mobile profile. Clicked it, and did not get the error message that I get on non-mobile. I don't think he's online atm to accept the invite, so I don't know if it actually worked, but lack of the error message leaves me hopeful.