How does the settling time affect the frequency components to be measured?
There's a difference between settling time, and response time constant. 

The usual definition of response time constant is the time it takes for the error between the present reading, and the final settled reading, to decrease to 1/e, after a step change in input.

There is no 'usual' definition of settling time, because it has to have a further specification for how well it has settled, so to 1%, or to 0.1% of full scale for instance.

Where there is no spec for the quality of settling, the usual approximation for settling time is 5 time constants. This is because (1/e)^5 is 0.7%, and if the specifier couldn't be bothered to define a quality, then better than 1% will probably do.

If a system has a single dominant time constant, then its frequency response will look something like   

The -3dB frequency, also known unfortunately as the 'cutoff frequency', can be calculated as \$ \frac{1}{\operatorname{timeConstant}2\pi} \$. In this case, 1/(0.02*6.3) is about 8Hz (you'll notice I'm using all the precision this sort of calculation deserves), where the response is -3dB or about 71%. According to this graph, the response at 4Hz is about -1dB or 90%, the response at 16Hz is about -6dB or 50%. For each doubling of frequency above this, the response halves.

The fact that 25% at 4Hz does not line up exactly with 29% at 8Hz, we could infer a number of things ...

a) the system does not have a single dominant time constant
b) the supplier is being very approximate in the figures
c) the 25% is a nice round figure, intended to be a safe worst case, and you will always get better results than that.

Note that the figures do agree to within a factor of 2, and for most engineers reviewing a cheap system measuring a physical quantity, that's probably good enough for the frequency response!

This graph assumes a specific type of system, a single time constant dominated system, and the disagreement between the various specifications would seem to suggest that isn't the case. So, do not assume this graph describes exactly what your sensor will do. However, all is not lost. The response graph will still look something like the one linked above. In a higher order system, one with several similar time constants, the frequency response will roll off faster once above the 3dB frequency.

If we assume their 25% loss of gain at 4Hz figure is 'more correct' than their 20mS time constant figure, you could have 10% loss of gain at 2Hz. So depending on how accurate you need it to be, it may be no good to you above 2Hz, or above 16Hz, that's for your accuracy specification to decide 'suitable'.