There is absolutely nothing wrong with putting a strainer on the discharge of a pump, you simply need to be aware of two things.

One: While the strainer can be downstream, it should not be located on the discharge nozzle of the pump. It is better to be located after the check valve.

Two:  The strainer will create additional back pressure on the pump requiring a slightly higher head from the pump thus reducing the flow rate.

It is also worthwhile to note that, when the pump can accommodate the particles in the pumpage, it is much better to have the strainer on the discharge rather than on the suction.