I just run a long handled Q-tip up inside from time to time to see if it picks up dirt. Usually the main issue is a seater picking up cast bullet lube and lead shavings. Occasionally jacketed bullets shave on a case mouth and leave a bit of copper behind, but it's not as big an issue. Mineral spirits on Q-tips will often remove dirt and debris without even removing the die from the press. I've got tens of thousands through my Dillon Square deal without ever removing the dies from the press.
If you store dies in a dank basement, you may need to add some rust inhibitor to them for storage. That probably should be flushed off before you use them.
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