I have a number of chips on the test list. I read the forum/sticky on them and I think I understand the level of care/packing requirements. What I didn't see was the cleaning requirements on thermal paste removal. What level of cleanliness is acceptable for test chips? If cleaning is necessary, is there a preferred or accepted method?

You want to remove enough paste to not be wet or sticky.

I use bum wipes. Literally.
Take one or two out of the package and spread them open. Let them dry. Most bum wet wipes are
Made from a soft cotton paper rather than harsh tree wood. It safely can remove paste without damage to the chip.

Just make sure you use unscented/perfume free.
Any fragrance is likely made of a petroleum acid. Safe for your skin, not so much for aluminium-tungsten heatsinks.

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I wipe most thermal paste off while the CPU is still in the socket. That way you don't have to handle them as much and it doesn't get on the bottom side.