Please check work table.
Check that in this table, wekk number really fits day of work.

I just had a look into the database.
The entry into the work table seems to be correct:

+------+------------+-----------+----------+-------+--------------+---------+------------+----------+--------+--------+------+-----------+--------+--------+---------------+
| id   | idResource | idProject | refType  | refId | idAssignment | work    | workDate   | day      | week   | month  | year | dailyCost | cost   | idBill | idWorkElement |
+------+------------+-----------+----------+-------+--------------+---------+------------+----------+--------+--------+------+-----------+--------+--------+---------------+
| 6332 |         30 |        35 | Activity |  2030 |         1747 | 1.18750 | 2015-07-31 | 20150731 | 201531 | 201507 | 2015 |    680.00 | 807.50 |   NULL |          NULL |
+------+------------+-----------+----------+-------+--------------+---------+------------+----------+--------+--------+------+-----------+--------+--------+---------------+

But the assignment for this entry does not exist any more.
It seems that work allocated to deleted assignments can exist in the database and is displayed in the reports but not in the real work allocation page.
The assignment was broken after a server shutdown during a commit by a user.
After that the assignment could be deleted while work was still associated with this assignment.
No manual database manipulation has been made.

Is it safe for us to delete the line from the work table without any side-effects?
Is there a kind of integrity check tool for the database?

Is it safe for us to delete the line from the work table without any side-effects?

Yes.
Then you should make some change on Activity #2030 to be sure that all consolidated data is correctly updated.

Is there a kind of integrity check tool for the database?

No