This is the quote that Anarch refers from Swordsmen:
"She is pretty," he said.
"She is not muchly trained," I said, "and there are doubtless thousands who would bring higher prices."
"Still, she is very pretty," he said.
"Do you wish to challenge for her?" I asked.
"No," he said. "I have a better."
Unless there should be some misunderstanding here, one might observe that such challenges are not frequent, and normally require almost a ritual of circumstances. For example, aside from the usual impropriety of challenging one with whom one might share a Home Stone, Gorean honor militates against, if it does not wholly preclude, casual or unprovoked challenges. Obviously a skilled swordsman would have an advantage in such matters, which it would be inappropriate, and perhaps dishonorable, to press. Normally challenges would take place to recover a stolen slave, to protect a mortally endangered slave, perhaps to obtain a slave once foolishly disposed of, without which one cannot then bear to live, such things. Too, there may be economic constraints, as well, for if the challenge is not accepted, one is sometimes expected, depending on the city, the castes, and circumstances, to pay for the slave, with a purse several times her value. Few potential challengers then care to risk a refused challenge, as it is likely they cannot afford the slave, and must then retire in embarrassment. Many other possibilities enter into these things, but these remarks, hopefully, will give any who might chance to peruse these several sheets a sense of some of the prevailing customs in these matters. To be sure, brigands, pirates, enemies, and such, are not likely to concern themselves with challenges, but are rather the more likely, as they see fit, to attack, and kill. Similarly, in raids, and wars, it is understood that the property of the enemy, or quarry, or target, including not only his livestock and slaves, but even his free women, is legitimate booty. A proper challenge, on the other hand, is more akin to a duel, sometimes even to the setting of a time and place.
As you say, it is like refining, stating that not always a challenge is proper, in fact it is not very frequent. Also clearly there are cases that are no-no's sort of speak: challenging someone from one's homestone, challenging someone who is not as skilled as you. Finally it also states the risk of issuing a challenge, as the other side might not accept it, but might instead indicate the girl is for sale, at a high price, a price one might not be able to pay and as such, might find himself humillated (it seems being poor in Gor is humillating)
Finally there also a quote in Nomads, when Kamchack asks why should he fight in the games of love and war, after being challenged to participate. It seems that if you challenge somebody in Gor, he may request that you provide a good reason, or something to entice him too (i.e. you want to challenge me over my girl, well put one up too)