It will probably work best if you cd into your TXT directory.
Code:
cd TXT
for file in *.txt; do
mv "$file" ../TXT.BACKUP/"${file}.backup"
done
Since you want to move them instead of making a copy, adding .backup at the end seems odd to me because the originals are deleted.
After the "in" in the for loop you could have a space separated list of files if there are a handful of particular files that you want to backup:
for file in one.txt two.txt three.txt