All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, is His slave and Messenger.
It is obligatory to wash the area of the Mus-haf (the hardcopy of the Quran) that was contaminated with the urine of the mouse, even if this leads to damaging the Mus-haf, and it is not sufficient to let it dry in the sun. Al-Haytami said in Tuhfat Al-Muhtaaj: “Some scholars held that if a Mus-haf is contaminated with an impurity that is not pardonable, it is obligatory to wash it even if it would be damaged as a result, and even if it was owned by an orphan. The obligation in this regard is further emphasized if the impurity came in contact with the text of the Quran, as opposed to coming in contact with the leather cover or the margins.” [End of quote]
Besides, Minah Al-Jaleel, reads: “If a Mus-haf is written with ink that contains impurity, it should be erased with pure (and purifying) water or burned.” [End of quote]
You are not obligated to do anything other than purifying the Mus-haf. As for the bad omen, this incident has no indication of that; you should refrain from thinking about this matter and ignore it completely. You should know that believing in bad omens and superstition is forbidden in Islam.
Allah Knows best.