I have found the solution. The object is a global container field showing a graphic (user interface icons). It is defined as a button and was given a tooltip.
In FM 16, this field is seen as a grouped object -- different from fm15.
The solution is to elect the field (no tooltip), then press the Tab key. This seems to switch the focus from the button to the field. Once I press the tab key, I can edit the tooltip.
Correction: That should read "select" the field -- not "elect".