Freeform Writing Exercise A1
This is because the sentence is saying "Marta goes and takes their order." - order, in singular, therefore you need the noun in the singular form "su pedido".
To use the plural it would have to say "Marta goes and takes their orders.", but this would imply that they had more than one order, which is not the case.
I hope this clarifies it.
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Test your Spanish to the CEFR standard