From my understanding of the mechanic...yes...but that unsure feeling that brought you to ask that question also brings up the fact that it sucks thematically. I mean, how you train out of being affected by the First World as a child?
Is it legal to use the ultimate campaign retraining rules to retrain a feat to fey foundling after level 1?
Some of the options . . . involve retraining features of your character that are essentially permanent parts of your heritage, such as a sorcerer's bloodline. The cost of retraining these things presumably includes magical or alchemical alterations to your body. The GM might rule that these changes are unavailable in the campaign, are only available under rare circumstances, take longer, are temporary, require some sort of quest, or are more expensive than the listed cost. . . .
As with all things optional, the answer is a definitive maybe. Check with your DM.
(Mechanically yes. But your DM may overrule this, which may make sense for the specific campaign. In the future, have background options written it into your back story, just not necessarily taken, and then retraining becomes more acceptable.) Good luck.
Given all the other things that you can retrain, I don't see a problem rules-wise in regard to training in or out of the Fey Foundling feat. As a DM, I would probably let a player take that feat as long as he has not established a backstory that contradicts the implied background of that feat.
Retraining away from that feat is even easier to explain -- the character has spent enough time away from the First World that it no longer has a noticeable effect on him.