I eventually figured it out:
mosquitto_sub -h 192.168.1.5 -v -t ArgyleCourt/Property/# | xargs -d$'\n' -L1 sh -c 'date "+%Y-%m-%d %T.%3N $0"' | grep --line-buffered "IrrigationTank\|BoreP\|Hub" | tee MQTT_TankfillMsgs.txt
... adding -line-buffered to the grep command will output the filtered MQTT input to both, file and terminal.
Thanks for hanging in there.