According to Gur Aryeh, why did Yehudah fear becoming an object of derision? The woman had not been a harlot, for Yehudah had designated her for himself!
Gur Aryeh (to 38:15): Nevertheless, it was not public knowledge that Yehudah had done so.
Why did the kid-goat play such a prominent role in this episode?
Rashi: Yehudah was being punished here Midah k'Neged Midah - He tricked his father by slaughtering a kid-goat and dipping Yosef's robe in its blood (37:31-32), so too he was tricked in connection with a kid-goat. 1
Gur Aryeh: Why interpret this way? This whole sequence of verses is extra. The Torah could have said merely that Yehudah sent to retrieve the pledge, be it using the goat or its monetary value. It emphasizes that Yehudah sent an actual goat, to show how these events were Midah k'Neged Midah.
Why did Yehudah emphasize, "I sent this kid"?
Ha'amek Davar: I sent a special kid, for I recognize that the woman is esteemed. Also the people realized it was not harlotry. This is why later, Yehudah knew that she is pregnant from him, and did not suspect that she had Zenus also with others.
QUESTIONS ON RASHI
Rashi writes: "'Let her take [them] for herself' - i.e., Whatever she has -- let her keep it." How else might I have understood it?
Gur Aryeh: It does not mean, 'Let her now take them;' for the woman had the items in hand already; and she was not being given anything now. Rather, it means, 'Let her keep, for good, the items that she has.'
Rashi writes: "'Lest we become an object of derision' - ... if you search for her any more." How else might I have understood it?
Gur Aryeh: Do not interpret, "lest we become a laughingstock if you successfully retrieve the pledge;' for on the contrary, it would be much better to retrieve these personal items, than to leave them there with her, where they might be recognized by others.
Rashi writes: "... For what else should I do in order to keep my word?" How does Rashi know that this was Yehudah's intent?
Gur Aryeh: If Yehudah was merely saying that he forgave her the pledged items [to avoid derision], there was no need to justify this by saying, "Behold, I sent this kid goat!" Rather, he meant that he was no longer obligated to search for her to keep his word.
