Gmail App on iOS shows badge count for unread Chats

At times, the Gmail app for iOS can display a hard-to-remove badge. The badge corresponds to a gchat message that was received offline. The badge is considered difficult to remove due to a series of facts:

1. gchat sends an 'email' to your Gmail when you receive an offline message
2. gchat messages do not show up in any inbox in the Gmail app; they're only visible in the browser
3. The "Chats" label does not show up in the side bar of the Gmail app, so there is no easy way to access the chats
4. Searching for "label:chats" only finds chats up to June 7th. Maybe they released an update then that stopped sending chats to iOS devices?
5. Being online 24/7 (for instance, using the Hangouts app) is not a good solution, as I do not want to be online 24/7.

The question is: is there any way to make this badge less annoying?

Possibilities:

1. Can you make the Chats label appear in the iOS app?
2. Can you make chats not send emails when you're offline?
3. Can you make chats received offline not count as unread?

My "Notifications" setting is set to "Primary Only." This affects both my iPhone and iPad.

Solution 1:

Inbox by Gmail solves this annoying issue! I've switched over my personal email accounts, and haven't had any problems since.