External Hard Drive Recognized as Time Machine Format

Years ago, I used this external hard drive to backup my Mac, and when I wanted to use the hard drive for normal file storage again, I just deleted all the backup files off the drive. Bad decision, this didn't completely format the hard drive of it being recognized with Time Machine. Every time I plug it into my mac, it has the Time Machine logo, and it only works on Macs, no Windows computers.

I would like to have it be recognized on every computer, but I don't want to format it of its data nor do I have a place to store all its contents so I can format it. Any other solutions?