With you making only about $2,000 from this job, I have to assume the rejection of the non-acceptance of the W-4 is due to the amount you make, which is well below the standard deduction of $15,000 for single and $30,000 for married filing jointly.
I would just build the $2,000 of income into the estimated taxes you already pay, though you may want to ask your employer what the defaults in the Square system are. They may have a better idea as to why.
Thank you for question @Mingo08
All the best,
Marc T.
TurboTax Live Tax Expert
28 Years of Experience Helping Clients
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