Your customer will be interested in knowing the history of their sync runs. All of the information within the UI is available within the API. Our product docs cover the UI features.
Each of the pieces of information in the image above is retrievable via API. To fetch the sync runs for a given sync configuration, query the List Sync Runs endpoint. The pagination parameters can be used to iterate through. The response for a given sync run will look like 
{
  "id": 94,
  "sync_id": 52,
  "source_record_count": 15,
  "source_record_updates": 12,
  "source_record_deletes": 2,
  "source_record_invalids": 1,
  "records_processed": 14,
  "records_updated": 13,
  "records_failed": 1,
  "created_at": "2021-10-20T02:51:07.546Z",
  "updated_at": "2021-10-20T02:52:29.236Z",
  "completed_at": "2021-10-20T02:52:29.234Z",
  "scheduled_execution_time": "2021-10-20T02:52:29.234Z",
  "error_code": "JSON_ARRAY_ERROR",
  "error_message": "The array field being used does not appear to be valid JSON...",
  "error_detail": "Please make sure the field \"custom_field:Users\" with value \"jim\" is formatted as a JSON Array...",
  "status": "completed",
  "canceled": true,
  "full_sync": true,
  "current_step": "Running Sync"
}
  1. Start Time - created_at
  2. Duration - completed_at - created_at
  3. Run ID - id
  4. Sync Trigger Reason - coming soon
  5. Source Record Count - source_record_count
  6. Invalid Source Records - source_record_invalids
  7. Changed Source Records - the UI displays the sum of source_record_updates and source_record_deletes
  8. Records Processed by Destination - records_processed
  9. Successfully Synced Records - records_updated
  10. Rejected Records - records_failed
  11. Status - status
Error information is captured in 3 fields—
  1. Error Code - error_code
  2. Error Message - error_message
  3. Error Detail - error_detail