"Have you seen my cell phone?"
That's pretty close. It's the difference between a completed action in any time frame (verb 了) versus a present state having come into being (sentence 了) with immediate relevance.
For this sentence we can simplify by saying that verb 了 would be like "did you see..." and sentence 了 would be like "have you seen..."
I wanted to put this information higher up on the page for the sake of convenience, but dafadllyn's comment below is on point:
I think it’s because 看见 is a result complement, i.e. 看 on its own means look but does not include actually seeing. 看见 means to look and see. See 见 is the result.
For verbs that include a result, I think past tense is more natural. For example, “I have seen” is more natural than “I’m seeing”. Probably with or without 了 are both fine for conveying past tense.
My sense is of it is as follows (though I defer to native Chinese speakers):
Using only sentence 了 (as in the sentence at hand) makes the question more immediately relevant to the present moment: Have you seen my cell phone, and by implication, can you now tell me where it is?
Using both verb 了 and sentence 了, on the other hand (as in the "book" example), is more an inquiry about life experience: Have you had the opportunity to take a look at her book? (I'm taking liberties with the translation to exaggerate the different sense.)
In the right context (and with the appropriate time phrase) the latter structure is also used to express ongoing duration: I've been living here for five years, and by implication, I'm still living here. 我在这儿住了五年了。