Select by Color is selecting more than one color

[allelopath]

I want to select only black but I get greys in the selection as well.

How do I select only black?

[Ofnuts]

Just reduce the threshold of the selection tool.

This said you are likely doing it wrong. The "gray" pixels are not gray, they are black, but partially transparent. They are very important, because they are the way the outlines look smooth.  

What you normally want is get a selection which is proportional to the opacity of the pixel (Layer>Transparency>Alpha to selection), or if you just want to change the color, use the alpha-lock  (checkboard icon in the "Lock" line in the Layers list), and bucket fill the layer (without any selection) with the new color.

See here for some more explanation.

[allelopath]

Thanks for your response. Very helpful