The term "knee damage" can encompass many different conditions and injuries so let's just examine at some of the more common ones you might be looking at:
Osteoarthritis
Osteoarthritis of the knee is when the cartilage in the joint has become thin or worn and the body is unable to "keep up" with repairs. Walking generally isn't going to cause this unless you are severely overweight or you're walking in unsuitable footwear etc. Quite the reverse - after a period of rest to allow for some recuperation from a flare up walking is recommended as it is a low impact way of building strength in the knee and is good for losing weight etc. Running on the other hand is significantly higher impact (walking means you experience ground reaction forces of ~ 1.2xBody weight, for running it's ~2.5xBody weight) and can aggravate the damage and you're also much more likely to experience various types of musculoskeletal injuries. Although offsetting that increased risk of injury is the potential for increased cardiovascular fitness from running vs walking.
This is much more common in older people as the body's ability to repair itself decreases with age.
Tendonitis
Patellla tendonitis is an overuse injury where the patella tendon (which connects to the bottom of the knee cap) becomes inflamed or otherwise damaged such as a loss of collagen in the tendon. Similarly to osteoarthritis walking is rarely a cause of this - typically it requires much higher levels of impact than walking alone can produce unless severely overweight or excessive amounts of stair climbing.
This can also happen in older people where it is the result of repetitive small amounts of damage over an extended period of time - and just like in osteoarthritis as the body's ability to heal falls away the rate of injury can exceed the rate of repair leading to chronic problems.
Avoiding activities that cause pain and keeping up with low impact exercises to improve strength is recommended.
Summary
Basically if you take a sensible approach - walking on reasonably flat surfaces, keep weight low, use appropriate footwear, and apply a modicum of moderation walking generally doesn't do damage to knees unless something has compromised the body's ability to "repair" itself to a significant extent. The benefits however are many and can actually help prevent damage by improving both the strength of the joint and overall health and fitness. So that 30 mins brisk walking a day is doing you far more good than harm.
