Removing semi-transparent pixels in Photoshop CC 2017

Question

Hand lettering scanned as an RGB TIFF, I'm trying to isolate the letters from the background.

My method for getting the text separate from the background follows these steps, except I forgot to get my artist to scan in grayscale, so starting in RGB mode:

1. Manipulate levels to get pixels easily separable into black-and-white
2. Select all > copy
3. Create new alpha channel
4. Paste into the new alpha channel
5. Load Selection > channel: alpha channel > "invert" ticked > New selection
6. Fill selection with black

The result:

Looks good, got the black separated from the white, but there are artifact-y looking pixels around the 5 that I can't seem to get rid of. If I add a stroke via the Layer Style menu, the artifacts catch the stroke and it looks awful:

The artifacts are mostly transparent and I can't figure out a way to select them so I can remove them, or do the reverse and just grab the black; the artifacts don't even show up in the selection when I command + click on the layer thumbnail:

Any suggestions for how to get rid of these artifact-pixels and just keep the black when starting from an RGB TIFF?

Answer 1

Between the steps 4 and 5, add a Levels step that'd adjust the tonal range of your image. Moving the Highlights slider (on the right) towards the center will make slightly grey pixels white. You can decide on how much to move the slider from the graph: your goal is to have a flat curve in there, something like this: