Right effort, eg. letting go of the hindrances, uphold proper attention, increase kusala, abound akusala, is the prerequisite of right mindfulness, goes into the seven factors of awakening, while Saddha (or sometimes calked Sila) can be seen as the area of right effort: letting go, surrender, in regard of senses.
It's here already Adhi-Sila, highered virtue, which does not take on what ever touches, will be given from the Givers (senses-media). One, how ever, knows touch, knowns impressions... there Satipatthana beginns, not holding or getting lost on one while overseeing that already died off.
In regard of noting: when careful reading the Maha Satipatthana Sutta, it's all about "know"-ting what one does, all the way. That's food for right investigation already, feeded by Sati. Doing such in certain verbaliced way in mind helps to get not lost, distracted, yet at certain point verbalizing will be to slow in regard of the many events turning up and decay. So not wrong to let go of such at certain state, when good concentration is reached and proper attention pure.
No right effort, no factors of awakening, no right remembering/keeping in mind, no right concentration... wrong release.
As long as Virtue isn't complete, saddha, isn't complete (house not left), meaning no right effort, the Samadhi-Section will not develop, how much ever one tries. Cause of this lack is wrong view, wrong association. There is actually the base of the depending co-arising path to release.