Configure email forwarding from Gmail to Salesforce for Email-to-Case

Ensure that the internal Routing Address (ex: Returns@acme.com) is valid and accepting inbound emails.

Follow the steps to Automatically forward Gmail messages to another account. Gmail allows you to automatically forward incoming emails to another address. So you can use the long On-Demand Email to Case Routing address as your forwarding address in Gmail.
 

Here's how to forward messages automatically:

1. Before you set up forwarding, you need to configure your On-Demand Email to Case and create routing addresses. Please see the Configuring Routing Addresses for Email-to-Case and On-Demand Email-to-Case article to do this. Once you create your routing address and save it to generate the Email Services Address (Auto-generated long email address), copy it and then follow the steps below.
2. Open up a browser and log in to your Gmail.
3. Click the gear icon in the upper right and select Settings.
4. Click the Forwarding and POP/IMAP tab.
5. On that page, in the Forwarding section, select Add a forwarding address. You can also set the filters from this section. Tip: You can also forward only some of your mail by creating a filter. Create rules to filter your emails.
6. On the Add, a forwarding address pop-up box, paste the long Email Services Address that you copied above and click Next.
7. Click Proceed on the Confirm forwarding address pop-up box.
8. You will see a message on the pop-up box saying that 'A confirmation code has been sent to verify permission'.
9. Click OK and leave the Gmail screen.
10. Open up another tab and log in to your Salesforce org. 
11. Click the Cases tab.
12. You should see a new case created with a Subject similar to (#667745483) Gmail Forwarding Confirmation - Receive Mail from <youremail>@gmail.com. (It may take a few minutes for the case to get created depending on your connection.)
13. Open the Case and you should see the Confirmation code in the Description field. Copy the code and go back to your Gmail.
14. In Gmail, you should be on your Forwarding and POP/IMAP tab. Paste the confirmation code in the box above the Verify button and click Verify.
15. Select the Forward a copy of incoming mail to <forwarding email> and Keep Gmail's copy in the inbox radio button.
16. Under IMAP Access, make sure 'Enable IMAP' is selected and click Save Changes.
17. You have finished setting up your forwarding, now test it by sending an email to your Gmail and a Case should be created.

For more up-to-date information on how to forward emails from Gmail, refer to the Gmail documentation: Automatically forward Gmail messages to another account.