I can't think of any database that will filter specifically for Market Prohibited gathered items but I might be able to help narrow your search a bit.

There are some words that will point you to many Market Prohibited gathered items but it's not going to catch all of them. Any gathered item with "Rarified" (collectables), "Oddly" (ShB relic tool quest materials), and "Connoisseur's" (EW relic tool quest items) in the name will be Market Prohibited (keep in mind that's not true of items with the same word used for crafting relic tools).

Carbonized Matter is Market Prohibited.

Gathered Materials for ARR relic tools, Aetherial Reduction and many of the big game fish are also Market Prohibited but there are no common keywords to help filter them. The closest filter to narrow down the list would be by level needed to gather the item (will be 50, 60, 70, 80, 90 or 100) but you're also going to hit gathered materials used in crafting that can be sold on the market board.

It's not the solution you're looking for but hopefully it will help a little.