That is an interesting challenge, then.
AFAIK, you refer to having placed the Generic Building as Autogen via SDK Annotator, so you must run the Annotator, open the custom photo-real imagery BGL, locate the annotation, then select and delete it there.
As you may know, 'Autogen' Generic Building scenery objects can otherwise be placed via BGLComp-xml methods.
IIRC, ADE will not
create custom-defined Generic Buildings (any more), but it can
place them.
BTW: Custom Generic Buildings created in SBuilderX can be converted from BGLComp-XML code to MDLs and placed via ADE.
FYI: IIUC, had the Generic Building been placed via BGLComp-XML, you may have instead:
1.) Run ADE
2.) Open the custom airport BGL for the location in question
3.) Import BGLComp XML-based scenery placement BGL(s) active in Scenery.Cfg that place Generic objects
at that airport
4.) ID'd the object
5.) Deleted the unwanted object placement from the placement BGL which placed that object via ADE GUI
6.) Saved the deletion and re-compiled the Generic Building object placement BGL file(s) into which a change was implemented.
IIRC, ADE may have a way to do this without manually editing the separate BGLComp XML placement BGL source code.
Perhaps Jon could advise us on whether that ability actually exists in the current 1.79x build of ADE to edit a separate placement-only BGL that would otherwise have been output by ADE via a "Split Compile" ?
GaryGB