The official documentation does mention that Google Cloud Pub / Sub resends messages to subscribers until subscribers acknowledge the message receipt when using official Cloud Pub / Sub Node.js client.
But it does not explicitly mention this for background functions if they return a callback error. Refer https://cloud.google.com/functions/docs/writing/background.
If it helps - My background function does not use the official Cloud Pub / Sub Node.js client since I get all the required info from the event arguement itself.