The mishna implies that one is allowed to receive payment for para aduma ashes (from the fact that it has value when you are mekadesh an isha with it -עיין ביש"ש שמפרש דפליגי רש"י והר"ן וכן הרמב"ם והראב"ד אם מקדש בגוף הדבר או בשכר שיכולה לקבל על הבאת האפר), but the mishna in bechoros says that one cannot receive payment? The gemara makes a distinction between the transporting from place to place that one can receive payment for, but for the actual sprinkling one cannot receive payment for. What is the point of distinction?
The distinction seems obvious. One cannot receive payment for the actual performance of a mitzvah, but can receive payment for enabling a mitzvah so long as they are not doing the actual mitzvah. Transporting the material is not the mitzvah, it merely makes the mitzvah possible. This peshat is mentioned in the Tosafos R"I HaZaken, but is not the peshat of Rashi.
Rashi implies that even if it is not the ikar mitzvah, there is still a prohibition to take payment. The only heter to take payment is for something that has a significant tircha, you can take payment for the difficulty of doing it. But when there isn't any major tircha, it is assur to take payment.
Based on Rashi it should be permitted even for a witness to take payment (so long as it is from both sides, so that it does not create a bias in his testimony), when it is a bother for him to come to court. In fact the Taz in Choshen Mishpat (on the rama in 34:18) says exactly that based on our gemara. The Rama allows one to receive payment to go watch something so that they can testify on it, but once they have watched the event, they cannot receive payment for going to court since after witnessing the even they are obligated to testify (and it is a mitzvah incumbent on them). The Taz adds that if there is a difficulty for the witness to go to court he can receive payment for that just as he can receive payment for the transporting of the ashes.
Upon further analysis of Rashi, it seems that the Rama is correct (and it seems that the Taz does not have a good comparison from rashi's peshat). Rashi writes:
בשכר הבאה האפר ממקום למקום ושכר מילוי המים דמילתא דטירחא היא ורחמנא לא רמיא עליה ושרי למשקל אגרא
Why does Rashi add the words "the torah does not obligate him"? Rashi seems to hold that the entire distinction between the transportation where there is tircha, and the sprinkling where there is no tircha, only applies to a type of mitzvah that is not an obligation on this individual. Meaning, there is no individual who is personally responsible to do the mitzvah of eifer parah, therefore we allow the one doing it to receive payment for his tircha. However, a mitzvah that is incumbent upon an individual in particular such as testifying in court about what they saw, cannot take payment even if there is a tircha involved in going to court. Based on this, one cannot use a heter of "tircha" to permit payment for Talmud Torah because the mitzvah to teach torah is incumbent on every individual. כנלענ"ד