Crisp Vector Rebuild of Logo

I have a single-colour logo that currently exists only as a fuzzy, low-resolution image. I need it recreated from scratch so it looks razor-sharp on screen-printed T-shirts.

Please match the original artwork faithfully, then make the following light tweaks: clean up all rough edges and adjust or simplify any tiny details that don’t translate well to print. The overall look and proportions should remain recognisably the same—just crisper, cleaner, and ready to scale without loss of quality.

The final file I need is a high-resolution, transparent-background PNG suitable for direct hand-off to my printer. Feel free to work in Adobe Illustrator or any other vector tool to ensure perfect lines; just export the finished piece as the requested PNG as well as an SVG.

Once delivered, I’ll drop the file straight into the printer’s workflow, so accuracy and clarity are essential. If everything looks pristine at full size, the job is complete.