Your screen is from the user-properties of the IE plugin and AFAIK there is no object-tab available - in opposite to the user-properties within the desktop client. By using the IE plugin maybe a macro could be used to change these properties.
I checked both 12.10 and 12.30 and Objects menu is not visible in either of those tracks, unfortunately I did not have an 11.20 track virtual environment up, but given both 12.10 and 12.30 have same behavior, this would appear to have been a conscious change if it was changed. I did check defect system and I did not see anything there regarding removal of it, so I am inclined to think if you did see it at some point, that was likely the bug. Hope this helps. I am not aware of any means to try to change the behavior here either, sorry.
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