While brass (or phosphor-bronze) is softer than steel, this does not mean that there will be no wear to the steel - even polishing with a soft cloth wears steel.

That said, provided the cleaning is not excessive, or repeated frequently, I can see no problem. I clean mine with a phosphor-bronze brush occasionally and it suffers no harm AFAIK. Seems to need about 20 pellets through it to settle down again afterwards though.

One point with the Bisley kit - the rod is steel so care is needed to prevent damage to the bore from the rod, particularly at the breech and muzzle.