That’s a great question! I’ll try explain it very simply. When people argue or disagree in a legal way, they have a dispute. The word “settlement” means they solve the problem and agree on something. So “settlement of disputes” means fixing the disagreement and making peace. This is the normal and correct phrase in legal English. The word “adjustment” usually means changing or fixing something small, like numbers, prices, or a mistake. It is not normally used for solving serious legal disagreements. So your sentence should be: “Our company is open to the settlement of disputes.” That’s the correct and natural way to say it.

As far as I know, adjustment is the process towards a settlement, so it’s more about modifying and correcting, until both sides are happy and a settlement is reached. So adjustment is the process, settlement is the ending.