Tyrion was making a joke – gilded armor does not contain a significant amount of gold, the no doubt master-crafted armor would be worth far more in its original state than melted down, and in either case would not have been worth enough to fund the Northern war effort.
And since you’re not the first person to ask me about jousts and ransoming armor:
Were tourney ransoms generally a form of collateral, to ensure prompt payment? In order to be of any use, armour needs to be a perfect fit, so another man’s armour would be of no use to the victor himself and would have very limited resale value.
As we see with the Mystery Knight, ransoming armor is not about being worried that someone else might sell it, although horses are a different matter, obviously, and the armor thing is not 100% (chainmail can be resized and human body shapes aren’t so wildly different that it’s always unusable). Rather, because a knight’s armor and horse are essential tools of their profession and prerequisites of their social class, no knight would willingly forfeit them and thus they are perfect collateral for a debt – the medieval equivalent of leaving your credit card for a deposit.
The other thing to keep in mind is the class expectations of the people involved – as noblemen, knights are supposed to be A. men of their word of honor (so being too pushy about repayment calls that into question), and B. not concerned about money (which means being too pushy about repayment is an issue, but so is not paying your ransoms). At the same time, noblemen also like cash to fund their magnificent lifestyles, so you need to make sure that you get paid.
Ransoming armor or horses, like handing over your sword when you surrender, is a way of resolving this tension: it allows both sides to pretend that this isn’t about money and that everyone trusts everyone else, while making sure that ransoms get paid on time.