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You'd probably only need to filter on if the host has been connected in the last 24 hours.

Copied from the reference at the bottom of the "Create/Edit Session Group" dialog:

$NOWThe current time but rounded down to the hour; rounded down in order to prevent constant recalculation
$2DAYSAGO$NOW minus 2 days; any integer can be specified for days

So this should work for you as the Session Filter: LastHostConnectedEventTime > $1DAYSAGO

This text is controlled by the resource value "BlankMonitorMessageFormat", which defaults to the value of "ApplicationTitle". Both can be changed in the Appearance tab of the Admin page.