Compensatory mutations are mutations that correct a loss of fitness due to earlier mutations. In some cases, such mutations bring their own fitness costs, but often they do not. Even when they do, it is irrelevant to the power of mutation and selection to produce novelty.
Explore Evolution claims:
the effectiveness of the second [compensatory] mutation is a limited-time offer, a coupon only good for the exact environment in which it was issued. If the temperature changes in the environment,* or if the salinity changes, a whole new fitness cost comes to light. The compensatory mutation now "codes for" a protein that doesn't fold properly under the new conditions. And if it doesn't fold properly, it doesn't work properly. Or, it may not work at all.
* This is what happens when your body "runs a temperature" when you have a cold. Your body is changing the temperature of the environment, trying to make it less hospitable to the invading bacteria or virus.Explore Evolution, p. 108-109
In contrast to the claims of Explore Evolution many compensatory mutations do not have hidden fitness costs. Their "example" is a bacterium which has a compensatory mutation that makes it more temperature sensitive, and therefore unable to cope with the increased temperature seen in animals when they have fever. This appears to be an imaginary example, and the compensatory mutations seen in Staphylococcus aureus allow them to infect mice as easily, if not more easily, than the wild type.
But even if there were hidden fitness costs, the main issue is that the mutant is fitter in the altered environment. It does not matter if the mutant is less in the wild type environment unless it is returned to that ancestral environment. Penguins and polar bears are fitter than normal seabirds and brown bears in polar regions, but unfit in temperate and tropical regions. This hardly means that polar species are less fit than their ancestors in more temperate regions.
An inquiry-based textbook could readily present a real example from the scientific literature, and encourage students to predict how compensatory mutations would affect a species' ability to adapt to other environments. Instead, it presents a made-up example with too little detail for students or a teacher to practice inquiry-based learning.