Transfers glycine to 5-phosphomethyl-2'-deoxyuridine (5-PmdU) to produce 5-Nalpha-glycinylthymidine (Nalpha-GlyT) on DNA as a step in the pathway leading to thymidine hypermodifications in the viral genome (PubMed:34522950). As a final result of the pathway of hypermodification, 5-acetylaminomethyl-2'-deoxyuridine (5-AcNmdU) substitutes for a subset of thymidines in the viral DNA (PubMed:34522950). These modifications probably prevent degradation of viral genome by the host restriction-modification antiviral defense system (PubMed:34522950). 5-phosphomethyl-dUMP in DNA + glycine = 5-N(alpha)-glycyl-dTMP in DNA + phosphate Belongs to the thymidine aminotransferase family.