As of now, there is no audit logged in to the Audits table when an emoji gets deleted. The only way to find out about this is through the mattermost.log. For example:

{"level":"debug","ts":XXXXXXXX,"caller":"web/handlers.go:101","msg":"Received HTTP request","method":"DELETE","url":"/api/v4/emoji/<emoji_id>","requestid":"XXXXXXXX","statuscode":"200"}

It will be better to have this information logged into the Audits table for System Administrators to have the ability to trace this information.