Best to start with "is your Trade dollar authentic" and then worry if the marks are authentic. How much does it weigh, is it attracted to a magnet, etc?
In the most basic sense, chops are small test punches used to check if the surface was a thin silver plating over a base metal core. If that's what these marks are, then perhaps someone felt the need to check the surface -- another reason to spend some time authenticating the host.
Well they don't look like they were made yesterday. There are books and a chopmark collectors club that could provide more info.
I think these are not easy to authenticate, unlike official countermarks, especially given the basic shape. Coins with many chops appear to have been marked every time they were presented as proof that the coin was checked. However, you can draw the conclusion that just having a mark was not proof enough to pass without being checked, so what would be the point to fake a chop (as in a contemporary fake)? If it was a recent attempt to give a "details" coin some more value, I would expect a copy of a more interesting chop.
I would conclude that the mark is authentic if the host is authentic.
Please share what you learn if you do check out some of the references.