I sent money through Apple Pay to someone who doesn’t have an Apple account set up. They said they received the money and it is not showing pending, but transaction completed. When I go into the transaction there is not a delete option. She wants to send me back the money and shows the money in her wallet but doesn’t know how to send it back to me. What is the easiest way to resolve this?
You’re referring to Apple Cash, not Apple Pay.
The cash was transferred.
Once transferred, the transfer cannot be rescinded and the cash cannot be recalled.
The recipient has an Apple Account.
Here is how they can: Send and receive money with Apple Cash - Apple Support
This to send the cash back to you.
Then both of you should probably go into Settings > Wallet & Apple Pay > Apple Cash > in the Accepting Payments section, select Manually Accept Payments. This as it cuts down on unexpected transfers and particularly scams.
Your post is not clear as it says you sent the money to an Apple Account not set up, yet you also said they received the money. It also says she wants to send you back the money and it shows in her wallet. It is not possible to cancel a transaction that has been received and if the Apple Account was not set up, then they would not have the money in there Wallet.
Do you know this person? Sending Apple Cash is only intended for family and friends and there are many scams when people get involved in sending money to others. There are also no protections like you would find in a Credit transaction, when it comes to a Cash transaction like that used with Apple Cash.
More information is here about the use of Apple Cash for Sending/Receiving money.
Send and receive money with Apple Cash - Apple Support
How to get my money back from Apple Pay transaction
