Adobe gives it a time stamp, so you can safely remove the t= query parameter from your static image request.
The t= query parameter (date/time in DigitalPulse Debugger) is used to populate the Time Zones report, all other metrics are calculated using a time that is set by the data collection server when the request is received. In your case it makes sense to remove it so you don't have incorrect data on the Time Zones report.