What could be the first check for a user who cannot delete one of her files?

The first check for a user who cannot delete a file is to investigate whether the immutable bit is set on that file. In Linux, the immutable bit is a filesystem attribute that, when applied to a file, prevents it from being modified or deleted. If this attribute is set, even the file owner, who typically has permission to delete their files, will find that they cannot perform that action.

Checking the immutable bit can quickly clarify whether the inability to delete is due to this restriction. If the immutable bit is indeed set, it can be removed by a user with appropriate permissions, such as a superuser or an administrator, allowing the user to delete the file as intended.

While file ownership is also an important factor for file permissions, the immutable bit specifically controls the ability to delete or modify the file regardless of ownership. Network settings and file compression status do not directly impact file deletion in local filesystems and are therefore less relevant in this particular context.