1. A computing system for checking data integrity of a data object copied between storage pools in a storage system by comparing partial fingerprints of data objects, the computing system comprising: a processor; and a memory coupled to the processor and including computer-readable instructions that, when executed by a processor, cause the processor to: schedule a series of successive copy operations over time for copying a data object from a source data store to a target data store, each of the successive copy operations being configured to copy a version of the data object at a different time than the other successive copy operations; generate a source partial fingerprint of the data object for a copy operation from the successive copy operations at the source data store using a data fingerprinting operation that creates a fingerprint from a subset of data of the data object, the subset being selected by a dynamic function that selects different subsets in response to an initialization parameter that changes with each successive copy operation and represents an offset or location within the data object so that the data fingerprinting operation samples different portions throughout the data object based on the initialization parameter to determine the subset of data for the fingerprinting operation; send the source partial fingerprint of the data object to the target data store; send new data contents for the data object to the target data store, wherein the new data contents are not in an earlier version of the data object sent to the target data store for an earlier copy operation of the successive copy operations; and create a target partial fingerprint of the data object at the target data store and comparing it to the source partial fingerprint sent to the target data store to determine if they differ and thereby indicate that the data object at the target data store differs from the corresponding data object at the source data store, thereby allowing incremental verification that the copy of the data object at the target data store is the same as at the source data store.