Do you have an original format that the logo was made in? I went to look at the larger version you have on your home page, and well it is in JPG format, which uses lossy compression, which means you never get original full detail back.
What do you have for image editing? Here are 3 free ones for Windows, from basic but easy, to more complex, but also more to learn.
(not to be confused with MS Paint built in, it is surprising a decent starter program)
MS Expression Design 4
Pretty basic, but free
This is for more than Windows, this gets closer along the lines of complexity as Photoshop, but free. There is a lot bigger learning curve.
Hopefully you are not like my cousin, who does all his graphical design in MS Word (I'm not joking, he just a month ago started learning Photoshop)
Anyhow, the larger, closer to more original (if not original) of the logo, the better. TBH, making transparency of the current ones on the site, will be quite noticeable as such.