Bob
Another thing you might try (assuming this is Mac version) is to delete it using AppleScript. I have found that this works in some cases in which trying to delete in the UI does not:
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tell application "InDesign CS"
tell active document
delete item 1 of the selection
end tell
end tell
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Copy and paste the above (between the dashed lines) into the Script Editor (Applications:AppleScript:Script Editor). Next, select the one object you want to delete in your InDesign document. Back in the Scripot Editor, press the "Run" button, and hopefully it will work...