Gmail – MX records for G Suite Gmail:The domain name must have a valid TLD label

When you set up Gmail to send mail as your other account, there are two choices:

• Use Gmail's SMTP server
• Use another SMTP server

If you choose the latter option, it should use your real mail server to send the email message. This should produce the same exact email message as if you logged in to your other email host and sent a message from there.

For information on how to use a different SMTP server, see Google's help document. Find the part that says If you choose to send mail through another domain's SMTP servers.

Google says that this is one of the reasons to use your own SMTP server:

Your Gmail address will still be included in your email header's sender field, to help prevent your mail from being marked as spam. Most email clients don't display the sender field, though some versions of Microsoft Outlook may display "From yourusername@gmail.com on behalf of customaddress@mydomain.com." For this reason, if you don't want 'on behalf of' to appear in any of your messages, we recommend using the SMTP servers of your other email provider.

Sounds like you are reaching an SMTP-MSA server instead of an SMTP-IN server. Possibly the MX records for the recipient domain are misconfigured.

Does this only happen when you try to send emails to one specific domain? Do you see the error if you send from a non-Gmail account?