It's a way of saying it. In your example sentence it works well if you simply leave the 'be' out, as Randy says. To all the grammarians out there, I have a question. What exactly are we dealing with here? Is this confusing because the 'published' has an adjectival flavour here? I like to see my paper BE published - I like to see my child BE happy. Or is there the passive feel of "I like to see my paper (BE) published BY somebody." There are a lot of constructions where the BE is added. Sometimes it is not needed. Sometimes it is the subjunctive. Sometimes it's old-fashioned. Sometimes these questions BE a real headache! (that's colloquial rural farmer talk! Just like The Wurzels!)

I agree with Randy. He gives a perfect answer for your question. If you were to include the "was" you might say... "I felt extremely satisfied to see that my paper was published in the school newspaper." (add: that) But it might change the meaning. Instead of being glad to see your paper appear in the newspaper, you would be MAKING SURE that it gets in the paper. Hope I haven't confused you. I'm just trying to give you another way to say the phrase.

"I felt extremely satisfied to see my paper be published in the school newspaper." Actually, the most natural sounding way of saying this would be to leave out the BE altogether: "I felt extremely satisfied to see my paper published in the school newspaper."

Actually, you can use any of the three. They all make sense, but in this case I would use "was".