To delete rows in a table, use the DELETE verb plus Horizontal Filtering on the primary keys(s). For instance deleting a contact: 
curl "https://integration.getmateo.com/api/v1/contact?id=eq.123" \ -X DELETE

HTTP/1.1 204 No Content
No response body will be returned by default but you can add a select query parameter to select the columns that should be returned: 
curl "https://integration.getmateo.com/api/v1/contact?id=1234&select=id,full_name" \
 -X DELETE -H "Content-Type: application/json"

HTTP/1.1 200 OK

{
  "id": 1234,
  "full_name": "Max Mustermann"
}