.trashes on my usb drive?

I often transfer files form my pac, to a pc via my 1GB Lexar USB drive. When I delete files on the drive while it is plugged into my mac, they appear to be gone. Howeve, once I plug the drive into a windows machine, the deleted files are present in a .trashed folder on the drive. This is problematic, because it reduces my storage on the drive, dramatically. I have to plug it into a Windows machine and find the trashes folder and delete it. How can avoid the trashes folder even being created? Can I format the drive into a different file format?