How do I clean the screen inside the high-pressure filter attachment I purchased from Lowe's? Should I open the end in the direction of the arrow?

You should open the item from the inlet. See image below.

To clean the inside of the high-pressure washer filter, follow these steps:

1. Turn Off the Pressure Washer: Ensure that the pressure washer is turned off and disconnected from the power source to avoid any accidents.
2. Relieve Pressure: Release any built-up pressure by squeezing the trigger on the spray gun until no more water comes out.
3. Disconnect the Filter: Unscrew the filter from the pressure washer by turning the connector at the bottom (outlet side) counterclockwise.
4. Open the Filter: You should open the filter on the inlet side, which is opposite the direction of the arrow. This typically involves unscrewing or removing the cap or fitting on the inlet side.
5. Remove and Clean the Screen: Once the filter is open, carefully remove the screen inside. Rinse the screen under running water to remove any debris or buildup. Use a soft brush if necessary to clean thoroughly.
6. Reassemble the Filter: After cleaning, place the screen back inside the filter and reassemble it by screwing the cap or fitting back on securely.
7. Reconnect the Filter: Attach the filter back to the pressure washer by screwing the connector at the bottom (outlet side) clockwise.