[jqr-]

I'm almost sure "pepinillos" is what's throwing her off. That's their proper name, but they're nor common in Mexican cuisine and therefore not part of the lingo. If ordering at an American place in Mexico, you would call them "pepinos".

Back to your example, both of these sound natural to me:

"Una hamburgesa con queso sin pickles" "Un/a cheeseburger sin pickles" Here the gendered noun can go either way since it's not clear if cheeseburger is a male or female noun. You: "Una hamburgesa sin pickles" Them: "Con o sin queso?" You: "Sin".

Source: I'm almost your target audience.

[papertokyo]

That would be raw cucumbers not pickled cucumbers, no?

[jqr-]

Correct, but since "pepinillos" is not widely used, "pepinos" is understood by context to mean the pickled variety.

This is the case for Mexicans in the southwest USA. Things might be different for other regions/nationalities.