As the lesson notes, in French there is a distinction between marcher and aller à pied.
There is the general act of walking for which 'marcher' is appropriate - it may be qualified by how, when, why or even 'where' as in a location for walking (je marche dans la forêt), but is not used for the specific act of 'walk(ing) to somewhere'.
The specific act of using walking as a mode of transport to get somewhere is « aller à pied ». Your example is about « going to somewhere (by foot/by walking) » and « aller à pied » is the best (precise) translation in this case.
What is your question?
It's unclear what it is you need help with?
Just to complement Maarten's answer: aller à pied always needs a destination. You can't just use it for the act of walking by itself.
You still don't mention any kind of contrast.
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