Good idea to remove the float for more room to fish. Make a wire with a hook, give it some time, you will find it. And, If it were my bike (have a K13) I would ride it and keep looking for the part it is not going to block the suction outlet. You are not the first to loose this trash basket. Not even sure why it was put there other than to cause aggravation. I pull mine out each oil change because I use a suction device. I don't bother with that little tube.
Mount Vernon, WA.
tire guy, I'll mount your tires.