How to 'feather' graphic image border into background color?

[TikiTorture]

I bought a simple black colored graphic from a website.  I didn't realize it wasnt transparent.  I used a web tool to lift the image off the white background so its transparent.  However when the image is placed on a black background, it effectively has a subtle white border around it due to the various greys used to feather the image into the white background.

What is the best way to change this image so that it can blend into the black background better?

 Thank you

[TikiTorture]

Here is the original

[Ton Frederiks · Accepted solution]

You could try to use Image Trace (or manual trace) and use Myriad Pro Bold and Semibold for the text.