Remove Background & 300 DPI Upgrade

I have four classroom graphics in PNG format that need a quick but precise touch-up. The white background on each file has to go so the images sit cleanly on any coloured surface, yet the teacher’s name currently rendered in white must remain exactly as is... (Budget: $10 - $30 USD, Jobs: Adobe Illustrator, Adobe Photoshop, Background Removal, Graphic Design, Illustrator, Image Processing, Photo Editing, Photoshop)