1. A method for maintaining data integrity in a computer data storage system by backing up and restoring one or more clone file trees in the computer data storage system, the method comprising: generating, by one or more processors, a clone management table that includes at least one clone file parent and at least one clone file child; recording, by the one or more processors, in the clone management table, a clone management information about each clone file in one or more clone file trees in a file system of a computing device, wherein (i) the clone file tree includes metadata specifying a sequence of files with parent-child relationships in which a given clone file child is generated from a given clone file parent that immediately preceded the given clone file child in the sequence (ii) the given clone file parent is modified to be a read-only file when the given clone child file is created and (iii) the given clone file child is a read and write file; responsive to receiving a backup request, updating, by the one or more processors, the clone management information, and storing one or more data blocks that are in the one or more clone file trees; responsive to receiving a request to restore a clone file, analyzing, by the one or more processors, the clone management information about the clone file, and restoring one or more data blocks in the clone file to the file system; responsive to receiving a request to restore a clone the parent, analyzing, by the one or more processors, the clone management information about the clone file parent, and restoring one or more data blocks in the clone file parent to the file system, wherein a given clone parent file contains all data blocks that were originally in a file when a clone of the given clone parent file was created; responsive to receiving a request to restore a clone file tree, (i) analyzing, by the one or more processors, the clone management information about the clone file tree, and (ii) restoring, by the one or more processors, one or more data blocks in the clone file tree to the file system of the computing device; and responsive to receiving a request to check a validity of the clone management table, analyzing, by the one or more processors, the clone management information in the clone management table for coherence, and generating a list of an invalid information that is in the clone management table, wherein the updating of the clone management information in the clone management table enables the backup and the restoration of at least a part of the clone file tree precludes one or more data redundancies and restores the clone file tree to a form that the clone file tree had when the clone file tree was backed up.