You don't

"Good day." You said simply and walked away.

She just stood there watching you for a while, then began walking after her partner.

You had an apartment nearby, you'd walked to the park from there and you could simply walk back, but at the growling of your stomach a restaurant stole your interest. Of course you could go back home and make a meal, it'd probably be far more healthy. But you'd also be alone there, and perhaps the chattering of people would drown out the despair you felt after such an encounter.