clip microphones suffer a lot from transmitting the vibrations creasted by the keys closing. They are of course connected to the body of the saxophone which, is hit repeatedly ( whether this is on rolled or straight toneholes is not important) by a flat surface impacting the body itself. How could this not produce noise?
As Others have suggested , cushioning the clamp would normally produce less such a problem but to so extent will always be there, just subdued. Another way to deal with this is to have an elastic mount of the microphone itself.
I think this is one of the most common reasons why people have abandoned the mount on body and bell in favor of external microphones.
SD systems uses all manners of cradles to isolate the microphone form its mount but still ( I think) the sound of the is audible if the volume is not overwhelming it.
http://www.bill-lewington.com/sdsys.htm
Suprisingly some folks are now trying somehting that was tried before and that is to build a piezoelectric pick up either in the mouthpiece or the neck ( the first being a less intrusive way to do this).
This completely different approach was discarded by many after its introduction in the ’60 ’70 with the many systems like Varitone, Octavoice and so forth.
If you watch this video you can hear its application and the near total absence of key sound , the sound is rather bright though but not all the mikes are the same, the P7 sounds very much better than the other ones.