The פשוט פשט would be that רבא holds that his יאוש at the end is מגלה that he was really מתייאש all along. However, this is very difficult as how does that work? In fact, the ראב"ד asks this should be תלוי on the מחלוקת whether or not יש ברירה.
Another way of explaining the מחלוקת is as follows. אביי holds that you need יאוש בפועל, the person has to actually be מתייאש. The fact that we know the person will be מתייאש when he finds out is irrelevant, until he is actually מתייאש it is still his. רבא, on the other hand, holds that since it is עומד ליאוש, the average person would be מתייאש in this situation , the Torah permitted you to take it even though there was no יאוש בפועל. In fact, the Ritva writes that רבא holds that יאוש שלא מדעת works even if the person is never actually מתייאש which fits in well, it is not dependent on him, rather the Torah was מתיר where it is עומד ליאוש.
We see from תוס' ד"ה דלאו בני מחילה (on 22B), that they hold like this as well. Tosafos writes that according to רבא there is no question from קטנים because when they grow up they are מתייאש. We can't understand the תוס' כפשוטו that the יאוש at the end is מגלה that they were מתייאש all along, because they were קטנים and could not be מתייאש. Rather the פשט has to be as we explained that רבא holds that since it is עומד ליאוש the Torah was מתיר and therefore the fact that they were קטנים at the time is irrelevant, because it is not dependent on their יאוש, rather the Torah was מתיר.