Lothian and Borders Police confirmed officers had moved on 20 to 25 people from outside the club.
Inside, party members voted 25 to five to reopen the selection process to find a candidate for the general election.
Elected in 2001, Ms Moffat has been a controversial figure. Activists tried to have her deselected in 2007 but their attempt was defeated by union block votes. The following year a motion of no confidence passed by the local party was ruled unconstitutional by Labour headquarters.