android-timestamp-keeper

Modern android devices don't use anymore Mass Storage Mode. Instead they use the internal sdcard as a virtually mounted subfolder inside /data partition. It would be ok if MTP preserved correctly timestamps, which doesn't. Other options that could work, like FTP with MFMT command doesn't work properly on android either.
Droid Explorer is enough for files, but doesn't support folders.

This handy bash script helps you to backup and restore the last modified timestamp for folders recursively.

If you want to use an android native app, there's File Timestamp, however the txt format is different.

https://play.google.com/store/apps/details?id=br.com.pogsoftwares.filetimestamp