Ours makes it easy. I remove the shackles, then put the halyard or sheet in a mesh laundry bag and just let it tumble for a while - just regular laundry detergent. I do the fabric softener in a bucket. Mix softener with water & just dunk the line then let it drip dry.
You'll find that the tumbling will show up any weak spots in the line cover - the core will pop out of any weak spots!