Welcome to the forum, ej.
I received the withdrawal yesterday, along with an e-mail titled "Your Kiva Withdrawal" from PayPal informing me that Kiva just sent me money. There was a "custom note" portion, which contained a message from Liz saying the withdrawal has been processed, contact her if any further assistance is needed, etc. So it took 3 days.
I'm still interested in knowing how they verify that it's actually going to you, especially if you enter a different e-mail address. Maybe there's a way to compare names through PayPal when sending money, despite different e-mail addresses. If so, that poses more interesting questions. Like what if names don't match; does Kiva not process the withdrawal and/or confirm with the account holder that they want it to go to so and so?

I also still think there should be some sort of destination verification when you put in a request for a refund. No e-mail address comfirmation, especially if you're requesting a withdrawal to a different address than your Kiva login, seems like a problem waiting to happen. What if someone entered a different address incorrectly/made a typo and their withdrawal went to someone else (assuming the e-mail didn't bounce)? That wouldn't be good.
The current Kiva Withdrawal Confirmation e-mail (sent to your login email) looks like this:
Dear [Your Name],
This email confirms your withdrawal request of $??.00. You can expect the funds to be deposited into your paypal account within 1-3 weeks.
We hope your experience loaning money to poor entrepreneurs has been a positive one. If you have any feedback please don't hesitate to share it with us by replying to this email. We read each and every email we get, and we'd love to hear from you!
Thank you,
Kiva Staff
I'd strongly consider changing that to something like:
Dear [Your Name],
This email confirms your withdrawal request of $??.00. You can expect the funds to be deposited into your paypal account
(withdrawalddress@goeshere.tld) within 1-3 weeks. If this email address is incorrect please contact us immediately.
We hope your experience loaning money to poor entrepreneurs has been a positive one. If you have any feedback please don't hesitate to share it with us by replying to this email. We read each and every email we get, and we'd love to hear from you!
Thank you,
Kiva Staff
And if Kiva allows you to send your withdrawals to a PayPal account belonging to someone else, then I'd change "your paypal account" to "the following paypal account".
Even better would be a different e-mail message
before this one, with a confirmation link that you have to visit. You've seen them before. In fact this forum sends one automatically to verify your registration before you can post. If Kiva had a system like this, then basically, you'd initiate a withdrawal, an e-mail is sent to your Kiva login address with a special link that takes you back to the Kiva site and verifies it was you that initiated the withdrawal process and double checks with you about the PayPal account it's going to. If all is well, you hit OK and the withdrawal process begins from there with a confirmation e-mail like the one above. An effective extra measure of security and verification.