All letters should be answered. Simply prepare the standard answer, which you can send to all the candidates you did not like and give it to your marriage agency. Politely thank him for his attention and inform him that he does not suit you. Do not write that you have already met someone else. Such answer threatens the reputation of the marriage agency, which published your announcement. Don't you agree that in this case it is more logical to send a letter to the marriage agency with a request to remove your announcement. Thus you would save the time and money of the man who hopes to receive a positive answer from you, and would make it easier for the marriage agency, saving them unnecessary explanations to the client.
How to eliminate? What characteristics should you rely on? There is no definite advice for this occasion. However it is necessary to pay attention to the following things: what is the letter about, as a matter of fact? To pay you a compliment? Does it contain unambiguous hints? Are you invited to friendly correspondence? Any other theme, which does not concern your desires to find a husband? Or you got a serious detailed letter with hope for a try to remember what photo did you send to the marriage agency. Did it contain an invitation to such letters? If yes, send another photo. But in any case give up such adventurers. Reading the first letter from the man, always remember: the person interested in your positive answer will for certain think over the contents of the letter, will try to send you a good photo, in other words, will try to make the first impression.