Hi Marsha, I couldn't find a way of removing individual items from the list, however, if you don't mind losing some entries, click the Tools | Options menu to open the Options dialog and under General | Project there is an option "Number of recently used projects to keep:" which defaults to 8.
If you change this value to 1, click OK, then restart Test Complete, only the last Project will be on the Start Page, removing old Projects.
You can, of course, change the value to, say, 4, to retain, for example, the last four entries.
Regards,
Phil Baird