Currently, if the Show Share Counts option is not enabled (on any button placement) we don't send a request to the API, therefore share counts aren’t shown in the backend.

If you don't have Show Share Counts enabled under your Buttons Share Counts settings, turning that option on should do the trick, however, that will display the counts on the frontend as well.

If you don't want the counts to display on the frontend, but do for the backend, enabling the Show total share count setting for your inline buttons AND setting the Minimum global share count to something like 10000, should then allow you to see your share counts.