I get notification for TB Sirate Starter update despite that I use new fresh drupal installation
Despite not using the distribution any more I keep getting the message to update TB Sirate Starter

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I had this issue before and yes, I took notes.
In my case it was solved by finding the culprit(s). They were jquery_plugin and jquery_update

# grep -r "tb_sirate_starter" .
./sites/all/modules/jquery_plugin/jquery_plugin.info:project = "tb_sirate_starter"
./sites/all/modules/jquery_update/jquery_update.info:project = "tb_sirate_starter"


The fix / workaround?

I deleted the directories jquery_plugin/ and jquery_update/

Then reinstalled them. 

# grep -r "tb_sirate_starter" .
# 


No more messages "Update Available - TB Sirate Starter "
And I think this is what the OP asked :)