One of the annoying things we’ve run into as an organization is that when a team is created in Microsoft Teams, it has to have an e-mail as it creates a distribution in the background tied to the team. What if you don’t want to allow people to e-mail that group?

I’m not saying this is the only option out there, and by all means if you have a different way please share it in the comments. This is just the first thing that came to me that worked.

You’ll need to login to your tenant through PowerShell. If you need help with that, you can take a look here. Once authenticated and logged in, there are two commands we are interested in.
The first command will hide the e-mail from your global address book. I’ve read that teams created more recently do this by default, but I’ve not confirmed, and it can’t hurt to do so.

Set-UnifiedGroup -Identity "GroupEmail@domain.com" -HiddenFromAddressListsEnabled $true

The next command will only allow mail to be sent to the group from an address you specify. Since I’ll never be e-mailing the group, I set it to my e-mail. Now, anyone other than whomever you set here will get an error when trying to e-mail the group.

Set-UnifiedGroup -Identity "GroupEmail@domain.com" -AcceptMessagesOnlyFromSendersOrMembers "user@domain.com"

Again, there could be other solutions out there but I didn’t find much in the admin panel, or on the Microsoft discussions. If you know of another way, please let me know.
At the end of the day, this achieves the desired result.