If the company could profitably charge more for their products, they already would be, regardless of what interchange fees (or other costs) were.

Raising costs means they need to charge more somewhere or lower transaction. Unless in monopoly situation, price pressure goes both ways.

If competitors can lower prices, whole market eventually ends up having to do that.

During the current inflation companies have used inflation as excuse to raise their prices way above inflation. It may be the same here. Publicly state that interchange fees are the reason for the increase but raise the price by way more than the increase in fees.