What effect does mindfulness have on dependent origination? What is the relationship between the three poisons of attachment, aversion, and delusion (Pali: lobha, dosa, moha) on one hand and the three links of ignorance, craving and clinging (Pali: avijja, taṇha, upadana) in the chain of dependent origination on the other hand? Does mindfulness have an effect on that?
The three poisons is what pollutes karma and turns it into asava. This polluted karma causes differentiation/hardening of the phenomenal world as well as of the inner world.

The three poisons are the first inkling of the "sentient being", accumulated in/as sankhara. Sankhara is what later develops into skandhas, from that grows bhava, which eventually culminates in "I am this guy".

The wrong mindfulness (in terms of "objects" and "I", opinions, side taking, self-interest, any kind of ego-centric thinking) - serves to keep the fire burning.

The right mindfulness (in terms of the four immeasurables and Bodhicitta, altruism, objective good, impersonal perspective) - leads to awakening and liberation.

Any action that is permeated with personal desire/attachment, personal aversion, any personal attitude - is polluted and leads to becoming.

Right mindfulness is cultivation of impersonal perspective. It leads to decrease of craving, obsessing, personal-goal-making, polluted action, reification, and identification.