On the official bug report forum, they have finally confirmed that courting gifts are not working properly under the influence system, and that a fix is scheduled for Game Update 4.1. Our romance-storyline companions should be interested in the courting gift category again by Valentine’s Day.
Courting gifts have been largely useless for the past few months, and that’s made them cheap. If you are following the romance storyline on any of your characters, buy gifts now to use or sell after 4.1, when they will again give the highest level of influence gain to multiple companions.
If you plan to romance companions, wait until after 4.1 to start Knights of the Fallen Empire: they are also promising a fix for the situation where romances are not recognized in the new content, but it won’t be retroactive.