Keep It
Attend as many limited events as possible and build an event trophy collection. You can have as many as 200. Display the trophies on your profile. The trophy acts as proof of your attendance and allows you to brag to friends. The trophy can be a "badge of honor." If you ever decide to trade someone else for a different account, having the event trophies on your profile can make your character seem more attractive to a new player.
Sell to Players
Post information about the trophy in the MapleStory forums and ask if anyone wants to buy it. You can also check Basil Market's wish list for people who want the item. Be aware that event trophies are rare but not incredibly difficult to obtain, so long as the player is able to attend any event. The trophies do not specifically represent an event, so a player will get the same one during any event. However, some collectors may be willing to buy the trophy, especially if they can't play during events. Expect only around 10 to 100 mesos.
Sell to an NPC
Non-player characters will pay more for your event trophy. Approach any in-game store and offer to sell the event trophy. Aim for 30,000 mesos. If the NPC offers less than 30,000 mesos, it may be due to your current server or town. Try another server. Prices sometimes fluctuate randomly. Hang onto the trophy until you can get the best price. If you hope to make more mesos, sell the trophy to an NPC instead of another player, who can earn a trophy herself.
Trade the Trophy
Other players may not be willing to pay a lot for the trophy, but they may be willing to trade items for it, especially if they're trying to amass a full collection of 200 trophies. Advertise your willingness to trade a trophy for a specific wish list of items on the MapleStory forums or on Basil Market. The more event trophies you have to offer, the more likely a collector will be willing to trade items for one.