Actually, that PARTICULAR version of "grommet" (which has 4 fold-over tabs on its underside) is part of a twist-catch fastener. That type of fastener has been in use since the 1890s right up to today. See the 1889-dated US Patent diagram, and photos of modernday twist-catch fasteners, below. They are most often used to attach a tarp or heavy curtain onto something else. My old pickup truck had a bed-cover tarp which used these twist-catches for attaching it onto the top of the truckbed's sides.