Noticed on SharePoint online that when a site is created without a office 365 groups i.e.
sts#3 template, you cannot delete home page web part and on lists and library’s you cannot save view as.
Has anyone else had this issue ?
What errors are you getting? Being connected to a group or not should not have an impact on this functionality.
Did you try this alternate way to delete webpart on any page.
Append ?contents=1 to end of url of page. https://contoso.sharepoint.com/sites/mysc/SitePages/Home.aspx?contents=1
It will open below web part page maintenance. Select webpart you wanted to delete(make sure page is checked out first) and click on delete.
P.S - If you are getting any specific error, please add details in question.