I got the same email today about the battery replacement credit. I had my battery replaced last year (2017) and had been waiting on this email for a couple months. The email had a link to "start the credit request", and it also said to be prepared to confirm my bank or credit card account information to complete the process. So, I followed the link and initiated the process. The first attempt ended with Apple's voice-mail system hanging up on me. The second attempt, I was connected with a real person. Only problem was, that person had absolutely no idea what I was talking about when I explained the battery replacement credit. She was convinced that the email I had received was fraudulent. She eventually said she would speak with her "senior manager". She came back on the line and seemed to understand why I was calling -- but she said that the funds would be returned to the credit card I used to purchase the battery. I said OK, but the email said I had to initiate the credit process. She said it would all happen automatically.
So, I have no idea whether I will ever receive a credit or not. But, I have lost a little faith in Apple support. My previous experiences with them (in the Apple Stores) has been mostly positive.
I hope others have better luck (and get their credit).
-- Steve
