Hi Ben,
It is quite common for traps to close when transplanting due to soil media, fingers or other traps setting off the triggers! Don't worry too much about it, the traps will reopen again in a day or two.
Only brown dead leaves should be removed. Even if the trap itself is nearing the end of it's life, all green parts of the plant will still photosynthesis and help the whole plant grow.
To avoid unnecessary trap closure in future, it is best to hold the plant in one hand by the white bulb and have the leaves together in the same hand, as displayed in this guide.. Flytrap Care.