To add some clarity and caution here:
To remove the magazine tube plug ("cap"), you'll need to remove the screws in the fore-stock tip cap and slide the cap off of the stock.
Otherwise, there isn't enough play in the assembly to get the magazine tube and plug off of the magazine tube stud.
And on the Model 444, there is a "whale belly" / "fish belly" / "stupid bulge" in the magazine tube, like on 1895s, that will prevent the tube from being slid in or out of the fore-stock without being turned 90 degrees so the bulge can slide through the gap between the barrel and magazine tube inletting.
(The bulge is to allow for feeding of wide meplats. It does have a useful purpose.)
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That being said....
The quickest and easiest way to tighten up a fore-stock rattle with a tip-cap style fore-end is to apply a little RTV to the front of the receiver. (The inner seating face, not the outer face where the RTV would be visible after assembly.)
Small bead.
Let it cure.
Test fit.
If the bead is too tall, trim it with a razor blade until the RTV gives you light tension against the tip cap.
It's not a permanent fix, as it'll only last 5-10 years. But it's cheap, easy, and quick.
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If it's a pre-'75 Model 444 with a barrel band style fore-end, the problem is probably peening and/or a stripped barrel band screw. (Marlin changed styles for good reason.)
The barrel band screw is too small for the forces that it sees with 444 recoil velocities, so it peens the slot in the magazine tube and the slot in the barrel, while getting bent. Over time, it opens everything up to the point that a major rattle develops.
And, separately, the screw is too soft and too small for the job. They are notorious for stripping (the barrel band isn't much better).
The best fixes involve custom parts and a gunsmith spending some time TIG welding and reshaping the damaged areas.
The easiest fixes involve cleaning up the slots, drilling and tapping the barrel band, and installing a larger diameter screw.