Is the fatwa considering "May Allah give you رجة [a tremor/shake]" as ill-mannered towards Allah correct, given that the speaker does not intend it as mockery?

Linguistically, "rajj" (رج) means violent shaking and intense movement, and from this is the Almighty's saying: "When the earth is shaken with a [violent] shaking" (إذا رجت الأرض رجا), meaning it is severely earthquaked and moved.

As for the ruling on supplicating with "rajj," it does not constitute ill-manners with Allah. It is similar to saying "May Allah kill him" or "May Allah earthquake the earth with him." The Prophet, peace and blessings be upon him, said in an incident: "They killed him; may Allah kill them." However, it is not permissible for a Muslim to supplicate against another without a legitimate শরعي right, because it is an aggression. Allah does not like the open utterance of evil speech except from one who has been wronged, nor does He love aggressors in supplication. The supplication of a servant is answered as long as he does not supplicate for a sin or the cutting off of kinship ties.