The Wilson Creek Museum's curator appears to be either uneducated or misinformed. It's sad that the average civil war Cavalry relics collector seems to know more about the relics than typical civil war museum staff do.
Persons wanting to CORRECTLY identify and time-date a military relic should pay close attention to the object's form/shape and its construction, meaning, what material(s) it is made of. Civil war horse-harness accouterment discs were made of either solid-cast brass ("bit bosses") or low-convex thin stamped sheetbrass filled with solder which held brass or iron attachment wires. In the Indian Wars era, the discs changed to having a sheet-iron back. By the early 1900s, that version was replaced with the type you found, which has no "back" component and uses integral fold-over tabs for attachment to the leather.
Creskol and DC Matt are correct, your stamped-sheetbrass horse/mule harness "domed" US accouterment disc with three integral attachment-tabs on its rim is definitely from the early-1900s through the present. Although the US Army almost entirely quit using horses around the start of World War Two, some are still used for Ceremonial purposes... which includes this version of horse-harness & US-marked accouterments.
The photos below show:
The civil war through Span-Am War solid-cast brass "bit boss" disc, with holed "ears" for attachment,
The civil war cavalry rosette having a solder-filled back with (badly rusted) iron wire attachment loops,
the Indian-Wars-through-Span-Am-War sheet-iron back, and
the 20th-Century "integral tabs."