Yes, a string being off center just a wee bit at the tips can have an effect on a bow's limb alignment, especially a recurve's. You should make sure the string is centered, and that the string grooves are symmetrical as viewed from every angle.
Also... we can't see it in the picture, but are you sure your handle is level? In your first picture, is the 'lean' all due to limb twist? What I'm getting at is, you need to be sure you don't have it held solidly at an angle, and then are pulling the limbs slightly sideways in relation to the handle. Between that and the string being off center, it could appear that there's limb twist when there really isn't much to speak of. That may not be the case, but I just want you to be sure before you begin removing wood.
What's the other limb doing? If it's pulling straight, then the problem is likely within the left limb itself.
Next is to check the accuracy of the thickness of your limb across its width. You can use a set of outside calipers, a dial caliper, a micrometer, etc. to do this. At any given point along its length, a limb should be the same thickness from one side to the other... at least initially. You may ultimately have to thin one side to get it to pull straight, but for now, check to make sure the stronger acting side isn't physically thicker. Check it in several places along its length.
People have a propensity to lean tools one way as they work. Through the course of tillering a flat bellied bow, it can cause one side to end up thinner than the other, which causes alignment issues. Again, this may not be the case, but you should check.
All that behind you, it's possible the thickness is right on the money and the wood itself is simply acting stronger on one side than the other due to how it grew. If everything else... string centered, lateral thickness, handle level, string groove symmetry, etc checks out, then you can either:
a) deepen the string groove on the side the tip is pointing towards (tip points to the weak side) as in Roy's illustration. After doing so, remove material only from the outer limb near where you deepened the groove, and only enough so that the area around the string groove matches the other side. Stay completely away from mid-limb while doing so. If that doesn't straighten the limb out, then:
b) remove wood from the opposite side (strong side) in either width(on the edge), thickness(on the belly), or both. If removing material from the edge, feather your strokes out so that you stay away from the string groove... you wouldn't want to have to deepen IT like you did the other side, which would be counterproductive.
It may help to think about it this way... the stronger side has more mass/strength on ITS side of the string. Plan 'a', deepening the string groove on the weak side... moves the string over, resulting in less wood/strength on the strong side of the string, and more wood/strength on the weak side of it... which helps to balance the limb's strength laterally relative to the force acting against it, the string... which straightens the limb out.
Plan 'b' shifts the balance of power toward the weak side by removal of wood/strength from the strong side's edge and/or belly... the result again... balance of the limb laterally, causing it to pull straight.
All that said, sometimes trees grow in such a way that it's virtually impossible to make them look/act perfect, and you'll ruin a bow trying to do so. Even staves and boards that seem nice and straight, with growth rings and grain (two different things btw) running the way we want them to, may never perfectly behave due to invisible internal 'predispositions'.
I worry a wee bit less about limb misalignment if the string errs to the arrow side, which makes it more 'centershot', easier to tune, and less critical of arrow spine.