There is exactly one reason to change the fixed cap that dangles from the air-variable trimmer cap that sets neutralization.
If you need to turn that cap beyond its minimum setting. That is, the best result you can get occurs with the plates fully apart. That would be the minimum-capacitance setting of the trimmer. Reducing the capacitance of that series capacitor will extend the range of this control in that direction.
This doesn't happen all that often with either japanese or american tubes.
Biggest root of this advice that I can see is sheer desperation. I suspect that the most-common reason this capacitor won't adjust properly at any setting from end to end has more to do with the choice of a so-called "pair" of final tubes.
The reason the neutralizing circuit has a variable cap in it is the variation from one tube to the next. Change finals and you'll find that the internal appearance has a big influence. If you use new final tubes that look EXACTLY like the old ones on the INSIDE, you may not need to adjust anything.
The 6JS6 tube was developed to use at around 15 kHz. The capacitor you get between the metal elements in the tube has no real effect on how the tube works in a color TV. As a result, those parameters were not controlled tightly from one brand to the next. Hey, it's engineering. Only spend money on features that pay you back.
The wide range of variation in these internal capacitors occurs because each factory that made them used a slightly different internal layout of the metal parts. Naturally this affects what size capacitor they behave like. The whole reason to neutralize the final tubes is because of the feedback INSIDE THE TUBE between input and output that these "piggyback" or parasitic capacitors will cause. That feedback will make the tube oscillate.
The neutralizing circuit takes a sample of the output signal and flips the polarity upside down. Feeds this out-of-phase sample to the input side of the tube. Get this out-of-phase sample exactly right, and it totally cancels out any tendency for the finals to oscillate.
If you haven't gone to sleep or hung yourself from a rafter yet, here's the payoff.
Both final tubes have to have the same accidental feedback level inside each one.
If one tube came from Pennsylvania and the other final came from Japan, you can be sure those internal capacitances are not the same. The proper setting of that neutralizing cap for one tube is NOT the correct setting for the other tube. There is no single setting of that adjustment that will make a mismatched pair of finals settle down and be neutral.
Oops.
Before changing that cap, have a look-see at your "pair" of final tubes. If the size, shape and color of the internal parts look alike, you're probably okay. The brand name printed on the tube has nothing to do with who built it. Only tells you who sold it. GE routinely sold RCA or foreign-made tube with the name "GE" on them. All the other brands did the same thing. It's the sales division that prints names on the tube. The factory ships them out in bulk with only the type number on it, nothing else. The name on the carton tells you who stuffed it into that carton and not one thing more.
The calibrated eyeball test is your friend here.
73