Where a claim that is required to be presented to the city in accordance with this chapter is so presented and action thereon is taken:
A. If the claim is allowable in full and the claimant accepts the amount allowed, no suit may be maintained on any part of the cause of action to which the claim relates;
B. If the claim is allowed in part and the claimant accepts the amount allowed, no suit may be maintained on any portion of the cause of action where, pursuant to a requirement to such effect, the claimant has accepted the amount allowed in settlement of the entire claim.