HomeRunner needs your Stripe Publishable key to take booking payments. The publishable key always begins with pk_.
HomeRunner does not need your Secret key, which begins with sk_, to take payments. Adding the secret key in your HomeRunner settings is optional. It only turns on card validation at checkout.
Before you send the key. Confirm that it begins with pk_ and that it belongs to the same Stripe account that is connected inside your PMS. The publishable key is designed to be public and is safe to share.