Yes, the "A05.08.07 Total Access 600 3rd Generation TDM Firmware" is the latest firmware for your particular TA624.
From the unit information you can see that it is a 3rd Generation unit (TA 624 Gen3), and it is currently running firmware A.05.03.05, but A05.08.07 is the newest FW available for the unit.
Hope this answers your question. If you need additional assistance you can just reply to this post.
Thank you for your help.