Ah yes, therein lies the problem. If you remove the macro via
Tools>Macro>Macros>Delete rather than by removing the module, then
Excel still believes a macro exists. Went into the Visual Basic Editor
just to verify that no modules existed.

However, if you first delete the module, then all traces of the macro
appear to go away.

OK, now I am stuck with several workbooks in which I eliminated the
macros using the logical but apparently incorrect way. So how do I fix
the situation? For example, can I go into Microsoft Script Editor and
do something useful?

I am using Excel 2003 SP2.