When Removing Mezuzos for Checking the old nails, screws and tape previously used to affix the Mezuzos may be discarded. However, Mezuzah cases and Mezuzah wrappings if no longer needed should be treated as sacred material and require Genizah / interment, after their use.
When removing Mezuzos for Checking, or renovations are being done, or for any other reason when the Mezuzah is remounted, the blessing should be recited only if the Mezuzah was off the doorposts for at least one night. If you are also adding new Mezuzos at this time, it is preferable to recite the blessing on a new one (providing that it is mounted on a door that requires a blessing).
It is preferred to have all of the Mezuzos returned to their original doorposts, or at least to the same type of entrance way (i.e., from one bedroom door to another, or from one archway to another) in order that you don’t lower the status of a Mezuzah that was once on a door required Midoraisa (Biblical) to a entrance way that is only Rabbinical.
A practical suggestion: when removing the Mezuzos, label each Mezuzah case with a number (using masking tape or the like). Tape an identical number on the doorpost from which it was removed. When the Mezuzos are remounted, match the numbers from your cases to the numbers on the doorposts.
