It's an interesting idea and I think it has potential.
Just some random thoughts:
I'm not sure about the idea of it working entirely through the fortune/luck attribute, it feels a bit un-Selish (the other known Selish magic systems let users program pretty much whatever they want). If you change it to "mainly fortune, but supported by other attributes" I could see that working in the setting.
I'm looking at Feruchemy for a list of usable attributes
Such as a knot for luck in sports increasing the target's Fortune, and also a little (Physical) Strength and/or Speed
Your "Persuasive" knot could work (in part) by increasing the Connection attribute between two people
If you want the system to be usable in combat (I don't think it needs to be) while still avoiding the "magic backpack" thing where a character just pulls out the perfect knot for every occasion, you could do something to limit the amount of knots a Knotbinder can or wants to carry around with them.
For example, if you add a rule that a tied knot grows more powerful the longer the Knotbinder carries it with them by absorbing their investiture over time, it allows for rapid deployment of a knot (i.e. in a fight) but it also prevents them from going around all the time with any knot you can imagine, because that would suck out too much investiture (leading to something like a Nightblood-sucking-out-your-soul-scenario).
Increasing the knot's power by weaving in a person's hair. I assume it's the hair of the intended target?
How does a knot without hair know who it's supposed to affect?
Is it purely the intent of the Knotbinder when cutting the knot?
Is the name of the target included in the knot's design?
Are both possible, but the way without a name limits how powerful the knot is?
Does a knot become more or less powerful with more specific instructions?
More specific would imply more complicated and thus more likely to fail.
For a group that tries to influence the future, their magic system appears to lack a means to know the future.
Unless they use a knot to increase their fortune/luck and then do some type of fortunetelling (Tarot cards, I Ching sticks, etc.)
The two groups of Knotbinders feels a bit limiting. In your place, I would make it three.
The majority of "Guards of Fate" you describe, who work together according to a grand plan. (Which offers the plot option of internal factional struggles about what the plan should be.)
The minority of "destructive rebels" you describe, who want to overturn the weave by causing chaos.
And another minority group who don't act according to the "Guards'" massive master plan, but just try to improve the lives of the people around them in small ways.
As JustQuestin2004 said, it could do with some more workshopping, but overall it's a very good start.
PS, hope I didn't overstep by offering suggestions that are maybe a bit too specific.