Hi Mark,
Thank you for your interest in Syncfusion products.
We are not able to reproduce the mentioned issue when Checked property is used to show check in BarItem. I have tested the issue with simple sample and attached in following link.
http://www.syncfusion.com/uploads/redirect.aspx?&team=support&file=popupmenu-1293666991.zip Please have look at the above sample and let me know if you still face issue. Could you please send us a minimal sample or reproducing sample that would be helpful for us to analyze the issue and provide a better solution.
Regards,
Lingaraj S.