Thanks to a prompt on Stackoverflow, I figured out what was wrong. As usual, assumption is the mother of all screwups!
I assumed "$wpdb->wti_like_post" converted to "DBprefix_wti_like_post", as "$wpdb->posts" converts to "DBprefix_posts". My assumption was wrong. It doesn't convert to anything at all, as far as I can see, presumably because it's not a built-in WordPress table.
What's needed is "{$wpdb->prefix}wti_like_post", which forces the DB prefix into place.
It works now.
Thanks very much to both commenters for the mental prompt from asking how the value comes out!