I listened 40 times.....sounds like he say Metto su l'acqua terla or perla or something similar and then very clearly la pasta............it should be PER )(like a pear} per...............la pasta but that's not what he said....He said perla.........cheeze................will I ever get this????
Its quite common in English to say "I put on the water" if it's in context........I put on the water for tea, or coffee, or pasta, or even in the 50s, I put on the water for a bath (wjen people put water on to boil for the bathtub) either way, I get the phrase, but this guy was not clear in his speech......it definately sounded like he said PERLA la pasta............that threw me.
Both should work in my opinion but: "The water" is of course the more literal translation from the Italian "l'acqua" and that is the way we need to think about how to phrase things in Italian but to translate back into English from Italian we need to think more about what is good English.
I have never encountered "put up" being synonymous with "put on" in the informal sense of "putting water on to boil". To "put UP" can mean to erect or raise, to propose, to pretend, to seek election, to lodge for a night or two, to put away or cease using. To put up WITH means to tolerate.
This doesn't sound at all as an idiomatic expression. We need to remember the prep. "su" that along with "metto" means "I put on water" with everything this implies. The problem with Duolingo is they neglect to go into specifics and nuances hoping its students are smart enough to get it anyway.
To have a clear understanding of what "idiomatic" means: idiomatic Definition in the Cambridge English Dictionary https://dictionary.cambridge.org/us/dictionary/english/idiomatic
(of a group of words) having a particular meaning that is different from the meanings of each word considered separately: an idiomatic expression. English Idiomatic also means natural in expression, correct without being too formal: His English is fluent and idiomatic.