Sydney Greenstreet did not receive an Oscar nomination for portraying the man who calls himself Mr. Peters in The Mask of Dimitrios.
Where Greenstreet played Gutman as an excessively astute figure who knew absolutely everything or at least acted as if he did. Greenstreet downplays the suaveness a bit in his performance as Mr. Peters who may know quite a bit but is more then anything else trying to figure out what he does not know. Greenstreet still has plenty of magnetism in this role though too and really his downplaying of it is a better for for the role of Mr. Peters who at first is only after some money through blackmail. Mr. Peters is a smart guy and Greenstreet plays him as such but as a smart guy with a rather simplistic plan without any grand schemes involved like old Caspar Gutman had.
The Mask of Dimitrios is a missed opportunity because the film comes in and out of Greenstreet and Lorre's investigation, instead choosing to focus on a series of flashbacks about Dimitrios which unfortunately don't even include Greenstreet when they very easily could have. As I said in my review of Peter Lorre in this film, Lorre and Greenstreet are great together. It is something particularly special just to hear these two guys talk to one another. Greenstreet is quite the master of exposition of any kind. No matter what the information may be, whether it really is interesting or not, Greenstreet is able to make something easy to listen do to his special voice and diction.
Peter Lorre in this film ended up being held back by the fact that he really had absolutely no character and really it was a good thing that Peter Lorre is such a character all by himself. Greenstreet actually has something to work with when it comes to Mr. Peters who has a bit of a journey as character while he takes a journey in tracking down Dimitrios. The character arc is relatively simple in that Mr. Peters is a first doing it for money then at the end does it for revenge, but Greenstreet is very effective in portraying this and finds why Mr. Peters would have the change of heart in the final scenes of the film where they find Dimitrios and his money.
When first they just find the money Greenstreet is quite amusingly blunt in showing the rather hollow moment of greedy lust as Peters almost seems to sniff the money. He quickly becomes moralistic when they find Dimitrios though. Greenstreet meets the extreme challenge though and alludes that the swing is caused by a strong hatred that comes from seeing the man who double crossed him face to face again. Greenstreet really carries the ending especially well particularly his expression of righteous indignation as he stares down Dimitrios with Dimitrios not having the upper hand for once.
Where Peter Lorre's performance in this film was an actor making something out of absolutely nothing Greenstreet makes even a little more by having just a bit more to work with. Again Mr. Peters is not an especially complex character and much of what makes him an interesting character is that Sydney Greenstreet is simply an interesting actor, but the little depth that there is to the role Greenstreet brings to life quite well. Greenstreet and Lorre both are always trailing the main plot in this film and technically they should be secondary in interest. The two actors' chemistry carries their half and actually steals the film as their simple final goodbye has more emotional power to it then any of the scenes depicting Demitrios's double dealings.