How does the Knight’s description of the stellar reputation of Arthur and his court spur the knights on to accept the challenge? How is hubris, or excessive pride, involved (ll. 257-338)?

The Green Knight is being passive aggressive here to get the desired response from the men. He talks of rumors that they are skilled fighters, courteous of people. The knights of the round table seem appeased by the Green Knight's flattery. Then the Green Knight calls out King Arthur's men for not standing up. This gets the Green Knight's desired response.