https://mafiareturns.com/credits/spend.php

Bodyguard Cleanup Perk (30 Days)

1.00 Credit

• Clean up useless bodyguards. Gives you a 20%+ chance to not have your timer used when you attempt to attack a bodyguard whose employer is dead. You are instantly able to do another.
• The 20% trigger rate goes up the more available targets there are, maxing out at 50%.
• Purchasing adds 30 days.

Your Attack timer wont perk unless they're (the player) is dead. Best time to see this perk work in all the glory is after a large war, and you're "cleaning up" all the unemployed BGs of the fallen.