When the T3i detects that a self-powered external microphone is connected, it should automatically switch over and disable the internal microphone.
Since this does not seem to be occurring I recommend resetting the camera's setting to default to see how it responds. The settings can be reset by following the instructions on page 176 of the camera's manual HERE.
For further assistance with this I recommend contacting our Technical Support team HERE.
07/31/2023: New firmware updates are available.
05/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
04/20/2023: New firmware version 1.4.1 is available for EOS R3
03/30/2023: New firmware updates are available.
2/07/2023: New product announcements!EOS R8 EOS R50RF-S55-210mm F5-7.1 IS STMRF24-50mm F4.5-6.3 IS STMRF15-30mm F4.5-6.3 IS STM