Disclosed herein is the preparation of reaction products which contain carboxylic acid-grafted functionalized propylene homopolymers and copolymers that can be used as additives for polyolefin-based plastic products such as hot melt adhesives. Such reaction product additives may be prepared by: a) providing a first reactant comprising a selected type of relatively low molecular weight, low melt viscosity, molten propylene-based homopolymer or copolymer; b) forming a reaction mixture by adding to this first reactant a second reactant comprising an unsaturated carboxylic acid-based functionalizing agent, and an initiator comprising a certain type of organic peroxide; and c) maintaining the resulting reaction mixture at a relatively low temperature between about 130° C. and about 165° C. for a period of time and under conditions sufficient to form a reaction product which comprises acid-grafted propylene-based polymeric material, and which has a relatively high Grafting Efficiency.