Assume there is a closed source application which uses Triple-DES with a fixed/hardcoded key to decrypt large amounts of data. Someone managed to extract the round keys from a process memory dump and was able to verify (using a patched version of 3DES that takes round keys as input) that these keys are actually able to decrypt the data successfully.
Is there a known way to use these round keys to reconstruct the original secret key from it? (As it is DESede, two keys are derived using decryption mode and one key using encryption mode). Technically, it is not necessary to be able to do so (a patched 3DES implementation can decrypt the data fine), but it would make the code more readable to just use normal 3DES and plug the original secret keys in. (Plus it would be possible to encrypt instead of decrypt with them).
If there is no such way, is it a design decision that reversing the derivation of round keys to be hard, or is it just coincidence?