Jordan's stated reason for not extraditing Al-Tamini is that her prosecution in the U.S. would violate the old Anglo-Saxon principle of double jeopardy, since Al-Tamini was once before convicted and imprisoned in Israel for the same bombing that gives rise to the U.S. charges. That excuse is complete rubbish. The U.S. charges are for the separate offense of murdering a U.S. citizen overseas, and the Justice Department appears to be confident they can prosecute her without implicating double jeopardy.
In any case, the idea that the King of Jordan won't extradite Al-Tamini because of some tender concern for English common law traditions is too ridiculous for words. He can and will act like a king when he wants to, and good for him.
Moreover, Al-Tamini's release from prison in Israel, although it is sometimes confused with her being pardoned by Israel, was obtained by means of the Gilad Shalit prisoner exchange. "Exchange" does not begin to describe that one-sided affair in which Israel gave in to political/emotional coercion by the terrorist group HAMAS. But, really, what else could they do? That small country is like an extended family, so to end the five year-long torment of one Israeli solider was worth releasing over a thousand prisoners.
All monarchies strike me as farcical, but the legitimacy of the Hussein dynasty of Jordan is even thinner than most. Why the Palestinian native population tolerates a British-imposed royal family that originated from elsewhere, I have never understood. (Of course, at least one Palestinian nationalist did not tolerate it.) Does the USG really need to placate them?
Well then, why doesn't the USG bring enough pain to Jordan to overcome its reluctance to extradite Al-Tamini? Presumably, the Biden administration (like its predecessor) must see some larger foreign policy interest involved that makes it willing to tolerate the dissonance of naming a top-wanted fugitive that it will not make a serious effort to capture.
I am realistic about the chances of a petition stirring up any action in either the Administration or Congress, but I'm signing it anyway. Al-Tamini has punishment coming to her from the fellow citizens of one of her victims, and I hope she gets it.