i just took apart my t370 a couple days ago and it should be identical…
of course, take off every screw on the bottom. Also, remove the battery and pull off those screws. And the power switch and identical nuckle plastic hinge cover on the other side. There is a screw under the plastic hinge on the left side and maybe right side.
The keyboard is held down by the 3 screws on the bottom of the system with the dot next to the arrow. After all screws are out, the keyboard is clips in by 2 tiny buttons above the F5 and numlock buttons (similar to a dell keyboard). Pry on 1 side of the keyboard and push each switch in. unplug the keyboard ribbon going to the board.
Next, 2 more screws holding down the subframe. get those out, pull out 3 ribbons and a push ribbon and pull off the subframe.
There is a wire going from the power subboard to the mainboard. untape it and pull it off. Now you can access the 1.8” HD.
This is all from memory, but i’m 90% sure its at least 95% accurate.