My first recommendations to not focus too much on those little, undetectable bumps. I do know what you are talking about, however. They are probably little pockets of oil sitting just under the surface of your skin. And sometimes even the clay mask cannot get rid of them—they have too much dead skin grown over them.
I realize this client is looking for a complete removal answer to her problem, albeit hidden bumps. Other than ignoring them (that won’t happen) or using the steps I’ve suggested, sometimes problems resolve over time. It very well could be something in her diet that is causing those places. Dairy can create small whiteheads or clogged pores on certain people’s faces. It could simply be an oil buildup that isn’t getting enough attention in her routine. Whatever the reason they exist, if she—if you—examine many different avenues in your life that your problem skin may be happening from, you very well may discover the answer to your questions.