JTR,
When you say "checks" what checks? To issue a type rating or for recurrent training?
It might not be that simple if your company does not hold its own approval and your going to a 142 center, as at the moment it would be that 142's centers TCE that is conducting the check.
With regards to actual "training" either in the sim or aircraft... A rated ATP can do it under the provisions of his licence as long as it is in accordance with your ops manual.
No separate TRI certificate exists.