No idea what you mean by grained. I'm guessing you're stretching the thumbnail images too large and is likely due to the thumbnail size you set being too small to begin with so the were stored very small. Adjust the thumbnail size globally within CB > Configuration > Images or for your avatar field it self in CB > Field Management. Changing those parameters will have no affect on existing images and those will need to be re-uploaded.

Regardless your install is 2 years out of date. I highly suggest you consider updating.

About the "Adjust the thumbnail size globally within CB > Configuration > Images or for your avatar field it self in CB > Field Management" if I set the css parameters directly from the CSS sheet, does not it work the same?

No, CSS just stretches or shrinks the image. It can't create pixels in the image that don't exist. They need to be uploaded in a more appropriate size if you don't want it to become pixelated.

Using CSS will distort the image. Resizing with CSS can't add or take away pixels. It just stretches or smashes it. Large sized images stored of course take more storage space and of course affect load performance, but in regards to avatars it's not going to be much of an impact as long as you'd not trying to allow users to have something like 2000x2000 avatars as that's completely unnecessary.