I removed the inner mesh from my MK319's (and did the Dorsey circuit upgrades to them). It actually wasn't soldered in in any of mine. I just bent it into a little roll with needlenose pliers and it dropped out the bottom of the headgrill.
Be aware that the outer mesh on the MK319 is very rigid and will 'ping' if you pluck or tap it. This makes it not so good for lots of things as it will ring sympathetically with some of the source material (certain pitches, etc.).
Scott Dorsey recommends replacing it with a more maleable (sp?) mesh altogether, which will reduce this tendency to ring, but for mine I just gave the headgrill a couple of light coats of paint (flat black) which dampened the mesh's resonance very nicely.
I prefer the sound with the inner mesh removed. It is more 'open', but a bigger improvement came by removing the black resonator discs from the front and back of the capsule (just do one at a time, carefully, and reattach the screws before moving to the other side). Together with the circuit upgrades these mics are now surprisingly useful.
I've used them on picked acoustic guitar, as drum room mics, and on some male vocalists with wonderful results.
JC