time-machine: selective file restore - I just want a few things from a TM backup that was made of another MacBook

So I have a Time Machine backup (on an external USB hard drive) that was made from a 2010 MacBook Pro. I think the computer was running the latest OS at the time the last backup was made -- Nov 2013, probably Mavericks, but maybe Mountain Lion.

There are some pictures in that backup as well as a lot of personal files. I would like to recover these pictures and personal files. The computer from which the backup was made has since been completely erased and reformated and sold. My only hope is recovering the files from TimeMachine.

I am now working from a 2014 MacBook Pro. I can connect the TimeMachine disk via USB and see it appear in finder, etc., but I can't seem to browse the backup and select the pictures and personal files that I would like to duplicate onto my new machine.