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I'm simply tryingf to mkake this image's background transparent>
Any guidance will be appreciated.

The image is in indexed mode - change to RGB Image -> Mode -> RGB

Give it an Alpha channel Layer -> Transparency -> Add Alpha Channel

Color select the black

Invert the selection Select -> Invert

Cut the selection Edit -> Cut

Kill the selection Select -> None

Restore the anti-aliasing Filters -> Blur -> Gaussian Blur with values 1 or smaller ( 0.8 works - enter that by keyboard)

The other way is just recreate the shape with a path, then stroke the path (but I was told off the last time I suggested that )

Thanks for your reply.
I followed your instructions, but 
Select -- None doesn't seem to do anything, and Gaussian Blur isn't available (greyed out)

any additional help will be appreciated

Did you put the image into RGB mode?

Not doing screenshots for that: A video - no audio - same as previous sequence.

Try Image>Mode>RGB (many things are disabled in color-indexed mode)

This said, I agree with Rich, doing it properly from scratch takes 5 seconds, botching something from the existing image takes 5 minutes.

Got it Thank you