Trophy Items are given to your Companions to raise their affection level for you. Depending on your companion it may or may not effect their affection level. This page here is going to give you a run down of each of the Companions and whether or not they like this gift. For more information on the specific Companion's likes and dislikes click on their link below.
Galactic Crime Lords Identity Card (Trophy Blue Item)
Splinter of a Rakata Stronghold (Trophy Epic Item)
List of Companions that like accept Trophy gifts.
Bounty Hunter Companions
Imperial Agent Companions
Sith Inquisitor Companions
Sith Warrior Companions
Jedi Consular Companions
Jedi Knight Companions