GO:0033743:   peptide-methionine (R)-S-oxide reductase activity
Catalysis of the reaction: peptide-L-methionine + H(2)O + thioredoxin disulfide = peptide-L-methionine (R)-S-oxide + thioredoxin. Can act on oxidized methionine in peptide linkage with specificity for the R enantiomer. Thioredoxin disulfide is the oxidized form of thioredoxin.