Hi Lucy,
Replacement of hardware peripherals such as Microsoft Arc Mouse wireless receiver can be accommodated by our Microsoft Supplemental Parts team. They can help you decide what would be the best option. To get in touch with them, you can visit this link to look for their contact information.
You may also refer to the "Replacements for damaged, defective, or lost Microsoft software or hardware" section for more information.
Let us know if you need further assistance.