Imagine that a person with anger throws Tefillin to the floor, but the Tefillin are inside two bags.
What are the Halachic consequences?
The person needs to do some serious character improvement, as we learn in Shabbat 105b that one who throws around his possessions in anger is heading towards worshipping idols.
רבי שמעון בן אלעזר אומר משום חילפא בר אגרא שאמר משום רבי יוחנן בן נורי המקרע בגדיו בחמתו והמשבר כליו בחמתו והמפזר מעותיו בחמתו יהא בעיניך כעובד עבודה זרה שכך אומנתו של יצר הרע היום אומר לו עשה כך ולמחר אומר לו עשה כך עד שאומר לו עבוד עבודה זרה והולך ועובד
Rabbi Shimon ben Elazar says in the name of Ḥilfa bar Agra, who said in the name of Rabbi Yoḥanan ben Nuri: One who rends his garments in his anger, or who breaks his vessels in his anger, or who scatters his money in his anger, should be like an idol worshipper in your eyes, as that is the craft of the evil inclination. Today it tells him do this, and tomorrow it tells him do that, until eventually, when he no longer controls himself, it tells him worship idols and he goes and worships idols.
It would probably be appropriate to fast or give the value of a day's worth of food to charity, even though the Chayei Adam (14:25) and the Aruch Hashulchan (44:3) say that this is unnecessary if the Tefilin fall while covered, here they didn't fall but were thrown.
Nothing has changed in the status of the Tefillin, if you check them that the outside boxes have not been damaged.
You could also try to shake them, and if nothing seems loose inside, then you're good to go. Otherwise get a Sofer to check that nothing moved out of place.