Various workarounds have existing in zabbix in the past to place hosts in a mode where it will not action on 1 or more of its triggers.  With the removal of the add hosts to group functionality on the hostgroup edit page, there's no immediate way from a dashboard to quiet a host for a relative period of time.  (Please correct this assumption if I'm mistaken).

I would propose an additional operation on the "Update Problem" page that would offer an option to quiet this alert or quiet this host.