This can be done via the frontend gui or in the yaml files - I’ll give you pointers to doing it in the gui .
Create an input_boolean (configuration -> helpers)
Setup your automation (configuration -> automations) to turn the input_boolean on when there is motion detected.
In the GUI editor -
Add a card to display the input_boolean (entities, entity, glance, button are probably reasonable)
Depending on the card you use, you may get a toggle switch or a default tap_action to turn off the input_boolean when you want to. Otherwise, you might have to configure a toggle tap_action.
Create a conditional card based on the status of your input_boolean, put a picture card inside it.
When you turn off your input_boolean the picture will disappear and appear again when the input_boolean is turned on by the automation
You could also / instead set up a tap_action on the picture card, so that when you tap it the input_boolean is switched off and the picture disappears.
There’s many more ways to skin this particular cat, but the above should work and each area I’ve mentioned has reasonable documentation.