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Relay is an alternative to slack.

Relay is open source, built on top of Mattermost. This means you can host Relay yourself. https://relay-chat.com/

Why would one want to use Relay instead of Mattermost?

Relay is actually hosted mattermost. Just a means to offload maintenance and uptime to someone working on it full time.

The part of software in Relay that makes mattermost SaSS is open source too.

Tell your team to stop spamming it around then please. Spam mattermost if you must.

They're not the team though.