What would you use to remove powder residue from inside a muzzleloader?

Using a cleaning jag is the appropriate choice for removing powder residue from inside a muzzleloader. A cleaning jag is specifically designed to push cleaning patches or swabs into the barrel, allowing for effective removal of fouling and residue left by black powder or other types of propellant used in muzzleloading firearms. The design of the cleaning jag grips the patch securely, ensuring it makes good contact with the barrel's interior surfaces to scrub away residue.

In contrast, the other tools mentioned serve different purposes. A bullet puller is used primarily for extracting bullets that have been improperly seated in the barrel or for safely removing loaded rounds; it does not help in cleaning. A nipple wrench is designed to remove or tighten the nipple on a percussion muzzleloader, which is vital for maintenance but not for cleaning the bore itself. Lastly, a bullet starter is utilized to help ram a bullet into the barrel during loading but does not address cleaning or removing residue. Therefore, the cleaning jag is clearly the most suitable tool for the task at hand.