A control variable is one which may, in addition to the independent variable, affect the outcome of the investigation and therefore has to be kept constant or at least monitored.
If a variable should be controlled, but isn't, then the experiment will not be a fair test. If it is very hard to control something - such as the amount of light coming through a window on a day when clouds keep passing overhead - then you should monitor this variable as well. i.e. record the light level through the window when you also take your main measurements; that way you can see whether it has affected the outcome.
By cutting part of the putty off, they would have been able to investigate different lengths, with no effect from other variables.