First off, welcome to RP. This isn't too much of a concern, I wouldn't think, if it is just time since your "rejection." I would certainly advise to stay away from not telling them as you suggested. By the context of your post, you have already applied (submitted your application), what did you put down for that question on your app? If/When the question regarding that arises, just tell them what you just told us. You simply don't remember what the reasoning for them rejecting you was. In my experience, the Agency wouldn't reveal that to you anyway. I could be wrong though. I say, don't let it bother you, go into your background interview, be up front and honest, and just explain to them what you just did here, and you should be all set! I don't see them holding anything like that against you.
Aoccdrnig to a rscheearch sudty at an Elingsh uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteers are in the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae we do not raed ervey lteter by it slef but the wrod as a wlohe. Initsenretg!!
Believe None of What You Hear, and Half of What You See.