“BackService” is an app downloaded from the Internet. Are you sure you want to open it?

Based on:

Accept or Deny "BackService.app"? - Apple Community

https://duckduckgo.com/?q=BackService&atb=v300-1&ia=web

It appears the app was downloaded as part of another app like Disk Drill.

Do you remember what you downloaded at that date?

Just what are you doing when you get the popup? This may help in knowing how to stop the popup in the future.

I would not install it especially if everything work fine on your Mac.

If you want to prevent the popup then:

Download and run this app so we can find more information about your installation.

https://etrecheck.com/upgrade

It shows what is launched and other information and is very useful in finding causes of problems. After you first launch the app make sure you check Enable full disk access in the box in lower left.

After running the app use the app's feature to paste to clipboard. The in the text box for a reply in this forum click on the addition text icon. This is because the normal reply text box limits how much you can type.

No personal identifiable information is contained if the app output. The app was written for a person who is contributor to these Apple Support Communities

Looks like Chrome wants to auto-install bits without telling you. This software would go into the "protected system" space if you approve it.

What does Google Inc have to say about BackService?