Polylactide-block-poly(gamma-methyl-epsilon-caprolactone)-block-polylactide (LML) is a sustainable thermoplastic elastomer (TPE) candidate that exhibits competitive mechanical properties as compared to traditional styrenic TPEs. The relatively low glass transition temperature of the polylactide endblocks, however, results in stress relaxation and low levels of elastic recovery. We report the synthesis and characterization of poly(gamma-methyl-epsilon-caprolactone) (PMCL) and LML end-functionalized with ureidopyrimidinone (UPy) hydrogen-bonding moieties to improve the elastic performance of these polymers. Although UPy-functionalized PMCL shows dynamical mechanical behavior that is distinct from the unfunctionalized homopolymer, it does not exhibit elastomeric behavior at room temperature. The addition of UPy endgroups to LML increases the ultimate tensile strength, elongation at break, and tensile toughness compared to unfunctionalized LML. Stress relaxation studies at a fixed strain show reduced levels of stress relaxation in LML with UPy endgroups. The stress relaxation was further reduced by including semicrystalline poly((S,S)-lactide) as endblocks with UPy endgroups.