I have solved the issue, though I don't exactly understand the precise root cause. I found the problem followed the Raspbian OS image and not the RPi 2 device as previously thought.
I was using a newer NOOBS generated Raspbian OS build for my second RPi 2 that didn't display the warning square on start-up. Both Raspbian OS builds were running with the latest firmware and software updates, but I noticed there were subtle differences in the boot-up sequences, including the default NOOBs settings used for RPi 2 clocking. When I swapped the microSD cards in the the two RPIs 2, the issue followed the card.
The card with the issue was a NOOBS generated Raspbian OS build originally created on a RPi B+. I then purchased my first RPi 2 and used the card from the B+ after I had first ensured it was running with latest firmware compatible with a RPi 2. At the time I thought the additional small square was a difference of the RPi 2 quad core Vs B+ single core. It wasn't until I acquired my second RPi 2 running a newly created build on a second microSD card, I noticed the difference and searched the web for more information.
Yesterday I built a new Raspbian OS build on third microSD card for my first RPi 2. Everything went as expected, and this time no small warning square on start-up. So it turns out not to be a real issue
Thank you to everyone for your help and advice.