You can remove an appointed supplier from a claim from the Appointed Suppliers section in the Claim Inspector.
Hover your mouse over the appointed supplier to reveal a "more" icon (three dots) in the top right corner. Clicking this opens a menu with a "Remove" option. Click once and then again to confirm you wish to remove the supplier.
After clicking to confirm, the appointed supplier will immediately be removed from the claim.
You can also remove an appointed supplier through the appointed supplier detail window, accessed via the "Edit" option on the contextual menu.
In this case, click the "Remove" button in the bottom left, and then click again to confirm.