By removing membership from the sites removes the list of sites in the "My SharePoint Sites". But I need to be the member of the sites listed under "My SharePoint Sites". To make this very simple I can give a senario.
When navigating to My Links -> My Sharepoint Sites, I see a list of sharepoint sites that I am a member of. One of the sites on the list is "Main Site" - of which I am the author/owner. However, I also see the sub-sites of the "Main Site" site - such as Subsite1, subsite2, subsite3 etc. on the list. This doesn't seem desirable. Is there a setting that I can use so the sub-site does not appear in the My Sharepoint Sites list?