For the most part, Reptilia just isn't really used as a formal taxon anymore. It may sometimes be used as a convenient grouping of more basal or less metabolically active amniotes, but in this way it usually applied to extant or recent groups (i.e., the classic collection of lepidosauria, turtles, and crocodilians) in which case there's no need to specify the inclusion or exclusion of early synapsids. The definition of reptilia as basically synonymous with sauropsida was an attempt to sort of preserve the term as a proper monophyletic clade, but in my experience researchers mostly refer to sauropsida instead to avoid any ambiguity.