Catalyzes the transfer of a methyl group from trimethylamine to the corrinoid cofactor of MttC. Co(I)-[trimethylamine-specific corrinoid protein] + H(+) + trimethylamine = dimethylamine + methyl-Co(III)-[trimethylamine-specific corrinoid protein] One-carbon metabolism; methanogenesis from trimethylamine. Can form a complex with MttC. Induced by growth on trimethylamine but not methanol or monomethylamine. Part of the mtbC-mttB-mttC and mtbC-mttB-mttC-mttP-mtbB1 operons. Belongs to the trimethylamine methyltransferase family.