Sometimes your position (heir, member of house, etc.) gains you influence points over a set group of people. However often you gain influence points that are not assigned to anyone - and it looks like the game allows you to wait and use them when you see fit. Is that all there is to it? In your games, can you just say "Oh, I want to assign my remaing 26 influence points to THAT GUARD RIGHT THERE please!"?? Or do you have to roleplay to get that influence/does it have to make sense/do the GM's decide? How do YOU handle assinging currently "unassigned" Inluence points?
In general, when I'm GMing, things have to make sense. You can assing a few influence points to That Guard Right There if you chat him up first, or threaten to kill his family or something, but assigning huge amounts of influence at one go requires one hell of a story to back it up with.
Note also that, as a general rule, a character may not have more than 20 points of personal influence over another character (pp. 190-191 DLE).
Things have to make sense in my games as far as rules go. For example, in D&D. If I hand out xp and someone levels they can't just learn to be a blacksmith in the middle of the woods, I make them find someone who can teach them first, putting points in already stated skills or one that makes sense they can learn at the time, or even what they have done to represent their skill since the last level. In another game a player was a hero from a tourney and was at attendence at the dance that followed and was asked to dance by the Lord's daugther. I intented this because he was a combat monkey and I wanted to make him alittle humble to the court, but passed pretty good for making crazy rolls, so he decided next level he will put a couple of ranks in Dance, since he got a slight reputation as being a good dancer.
Influence is another matter though, since its so new, but with your example I would make them rp it if they have any chance of it working, its not so easy to can trust or everyone would start the game influence in the Robert Baratheon or Tywin Lannister. If and player told me he wanted to put 26 points in a guard then he better walk up to him and tell him that you have proof that (SPOILER)he helped Tyrion escape Kingslanding and you will present it to Cersei if he doesn't cooperate