It took me over a minute, so my method wasn't the fastest. But the sentence plays on meaning, which I found to be tricky.
For the first blank, we are looking for a positive word that conveys the valuableness of environmental systems, 'bolster' is the only choice in the list that means to support or buttress. At this point, I wasn't sure of the second word, so I moved on to select the answer for the third blank - 'peripheral' - which aligns with the notion of 'extraneous systems'. At this point, I re-read the excerpt and realized that the first sentence needs to express an idea that is opposite to second sentence. 'Hotly dispute' would not be meaningful because the managers already admit that the systems are valuable. Both 'uncritically accept' and 'appropriately acknowledge' express a more positive meaning, but the word 'claim' after the blank made 'uncritically accept' a more appropriate choice. Also, all the words read together perfectly supports the conclusion that it is not the 'mere presence of a system' but individual managers' deliberate actions that can result in environmental improvements.