We have been entrenched in a battle with the Syndicate for years. What they lack in skill they make up for in numbers. It's impossible to kill them off fast enough to have any noticeable impact on their population!
We've found that the best way to deal with their size is to pilfer their emblems. Once an emblem is stolen the shamed member is 'dealt' with internally.
Pick their pockets clean and turn the emblems in to me or one of the other guards.