Hello Muhammed. It's probably the structure of the clause that is confusing you. It basically means, "Jealousy had a bad influence on their lives." Hope that helps!

Not a phrasal verb or idiom. There is an emotion called jealousy, when someone wants to be like someone else or do as well as someone else but can't, and is jealous of that person. A malign influence is a bad or evil influence, something that affects people negatively. ""the malign influence jealousy had on their lives" is talking about some people being affected negatively by jealousy.