Influence can be generated by appointments or by NPCs in very high places (King). There is no formal system to allow players of high station to grant influence to others in recognition of something.
A character that performs a task for another is granted a boon this boon can be re-called at any time, and the character returns the favour. If the character refuses he suffers a penalty and the boon remains and can be used the next month. This is a minor refusal, if the character refuses a second time, he is disgraced. Boons cannot be used to ask something that is not influencable.
e.g. a character wants to join the King's Musketeers and asks the Colonel for a favour to join. If an NPC had been running the unit, he would have required a L3 influence. If the Colonel grants the request, he may make a L3 request of the character any time in the future, boons can be traded like influence. If Influence Commodity is in force.
In order for the Colonel to retrieve the favour, then the character must be in a position to do something. e.g. If the character (now a captain) becomes the adjutant to a Lt. Gen the colonel can ask him to use his "influence" (the one task that an aide gets per season) in exchange for the boon. As the Lt. Gen is normally a L5 the L3 Boon is not enough to cover the cost. So refusal is not necessary, however granting the favour will generate a boon (another L3) in the other direction (as it was under strength).
Characters can offer boons not to reveal information, etc. e.g. a character is caught poltrooning on the field. His commander (or any witness) can be offered a boon to not report him. (or it could be automatically generated if the proper procedure (in this care reporting the offender) was not done.