I use a thread catcher with a weighted top to rest on the right side of my machine. I put sand in the top and it stays put.

I was given a wire pencil holder and I use that like a small waste basket to put the threads in.

Once I ordered a sticky plastic mat from a industrial supplier for this purpose. At the time these were used in hospitals, the tacky surface collected dirt from shoes. I placed it at the doorway of the room. You could tear off top page like a tablet when soiled. My sewing room was upstairs and I wanted to keep strings and lint from tracking downstairs.

I just keep one of those sticky rollers in my sewing room so that I can roll the threads off before I go downstairs.

If I remember . . .

If I worry enough about threads to do it . . .