If you look more carefully at the connector that goes into the computer, there are three black rings on the plug. Each one of those rings is for input or output. Two of those rings are for stereo output and one of them for microphone input.
A normal stereo headphone will have a plug with two black rings. A microphone will usually only have the one ring on the plug. So if you use this Y cable from Amazon, you should be able to use only the Microphone (pink) plug and be able to have sound input without connecting something to the green headphone plug.
And I believe you are confusing the Displayport
on the back of the T420s with an eSATA port