I bet epenguin is correct. My guess is that it is a way to eliminate the error of contamination from previous samples, and to preserve the molarity of the samples to be as close as possible to their expected value.
You do know what M means - moles/L. Butanol has a molecular weight of 74.12g/mole. Approximately a 0.1M solution has 7 grams and an 0.8M would have about 56 grams of butanol. You could calculate more exacting values.
If you wash the device or not, whatever adheres to the device is brought into the next sample.
Estimate how much residue would be left on the device after checking a sample, with no washing, and then calculate how much this residue would change the M of the next sample, if you go up or down.
See if the percentage error due to contamination is different going up from going down -is it less, or more?
Does the percentage error vary as you progress from sample to sample, or is it constant?
That might be the answer.
It probably does not make that much of a difference for your experiment, but for an exacting experiment it might be something to genuinally consider.
( Also, as a final note, a possible error could come about if you do start at the high value of M, that a drop of the high M liquid that you do not notice clings to the device and does not drop until you measure a lower value, which could just skew things up. )