Use a selection tool to select the background, then cut it out. Most programs have a "magic wand" tool, but even then, you might have to do manual adjustments.
It's kinda confusing. I'm using Paint.NET right now. Whenever I try and select the background, it also counts the vector as part of it. I tried using the magic wand as well but I can't seem to completely remove it from the surrounding image. :/
In Paint.Net, I ended up zooming in on the image and using the eraser tool-making it smaller for the fine details. Remember to save the image as a .png instead of a jpeg-jpegs have a white background and will undo all your work.