Select the measures, and use the 6 and 7 numberpad keys to move all of the notes down or up, a step at a time. Be sure to check your accidentals!

What do you mean, transposed? Do you mean that the key signature is correct but the notes have been moved up a third? If so, then Mike's suggestion is one of the possibilities. If the section is in the key which is a third higher than it should be, then you should use the key signature tool: select the transposed section, invoke the tool, choose the correct key, making sure the option to transpose up instead of down is selected.

Ok. Is there a way to select an entire section at once as opposed to individual measures?

… A number of consecutive measures in the following movement have been transposed up a third as a result of this key change …

My first guess would be that Finale’s handling of major keys and minor keys is at play here.

Try this in a new document:

Set the key signature to A minor.

Enter some notes.

Select All, and change the key signature to C major.

Now all the notes have been moved up a third.

In Other Words:

If the region that has been moved up by a third, is now in a key signature of a major key, then change the region’s key signature to the parallel minor key.

The key signature will look the same as before, but the notes will move down by a third.