The limited ability of mammals to regenerate has garnered significant attention, particularly in regard to skin wound healing (WH), which is a critical step for regeneration. In human adults, skin WH results in the formation of scars following injury or trauma, regardless of severity. This differs significantly from the scarless WH observed in the fetal skin of mammals or anamniotes. This review investigates the role of molecular players involved in scarless WH, which are lost or repressed in adult mammalian WH systems. Specifically, we analyze the physiological role of Anterior Gradient (AGR) family proteins at different stages of the WH regulatory network. AGR is activated in the regeneration of lower vertebrates at the stage of wound closure and, accordingly, is important for WH. Mammalian AGR2 is expressed during scarless WH in embryonic skin, while in adults, the activity of this gene is normally inhibited and is observed only in the mucous epithelium of the digestive tract, which is capable of full regeneration. The combination of AGR2 unique potencies in postnatal mammals makes it possible to consider it as a promising candidate for enhancing WH processes.