Did you interview a while ago? If so, it’s likely your post-interview file has already been reviewed and decided on by the AdCom so they aren’t really interested in an update that won’t affect your match chances anymore.
In Texas, LOIs really don’t come into play until there is waitlist movement; since that, of course, hasn’t happened yet, they are still open to receiving LOIs as you said was implied on your phone call.
If the update is really stellar (prestigious national award, publication in a respected journal, etc.) then go ahead and send it. The wow factor of the update might impact your outcome. But for any update that is just fluff (more service or clinical hours, why McGovern is for me, etc), it is historically not worth sending.