First... Are these yours? Did you make them? If not, you should provide credit. Not only because it's the right thing to do... but also because if we know who made them, we have a chance of getting the original sizes...
To take a very pixelated image like that and "clean it up" would take a great deal of effort. It would be much easier to take the raw/original files, and then resize them more carefully.
Try and find the originals. Whoever resized these did a painfully careless job of it.
Edit: One thing to consider... at that size, it may suffice to simply blur the image slightly. It'll smooth the edges, and shouldn't affect the rest too much.