There is no such thing as a file that cannot be edited.
If a file can be read it can be edited.
However, there are ways of making it possible to know if a file has been edited - i.e., to integrity check the file. To make it hard to edit a file and maintain the intrinsic integrity of the file.
The simplest method is to create a checksum of the data in the file and store that in the file as well. If the data is, for example, a CSV file, you could include in each row a checksum of the data in that row as an extra column. If the data gets changed the checksum will no longer match. Of course, that doesn't preclude someone calculating the new checksum and entering that. So maybe adding a checksum of all the checksums at the end of the file as well so you know if any checksums have changed.
Again, it's possible for someone to recalculate that checksum as well.
The most secure method is to digitally sign the file (in the way the PGP or GnuPG does). Without the private key, it's impossible to re-sign the file after modification. However, that kind of operation is comparatively heavyweight and not something an Arduino is particularly suited to doing (I'm not sure if it's even physically possible given the lack of resources an Arduino has).