When you get a new companion during the story, you can't be sure whether they're temporary or permanent.

There's no way to tell without story spoilers.

They often have an Influence of 1, though some do have an Influence of 10.

So I try to give them gifts.

All of them take the gifts. But you don't know until you check whether or not the gift increased Influence.

If the companion is temporary and can't receive gifts, disable the gifts or otherwise don't let them get used.

All of them take the gifts. But you don't know until you check whether or not the gift increased Influence.

In my experience, only the ones who join you in Onslaught will ignore the gifts. I don't bother with gifts on Ossus because rank 10 is strong enough, but Arn shows up at rank 1 for the Corellia FP, and that's a bit weak given the aggressively glitchy nature of combat there.(1)

(1) Last time I did it was on a Jugg, and I swear I met enemies who would "evade" away from about a foot from me to a distance of 30 cm from me.

Addendum. A foot *is* 30 cm, give or take not much at all. I was in combat with them right where they were originally standing, so they kept just resetting.

In my experience, only the ones who join you in Onslaught will ignore the gifts.

I've had this problem several times before Onslaught, such as in KOTFE with Rank 1's.