Exactly as everybody's answers. In short, claiming zakat means we are not paying the government any tax for the amount of the zakat.
When you say the money return you received is part of the 500 dollars zakat, that is totally incorrect. The 800 dollars return is from the total tax you paid to the government (you know that the government took a portion amount of money out of your paycheck right?) And you are claiming back these money. It has nothing to do with the zakat money.
Claiming zakat or donations means we are telling the government that we are not paying taxes for the amount we donated.
For example, if you pay zakat or a charity for 500 dollars, you will pay 0 dollars to the government because you don't have to pay tax on donations.
On the other hand, if you decided not to pay any zakat or made any charity contribution for that year then you would have to pay the government tax on that 500 dollars (X% of that 500) you keep or earn.
So remember to always claim your donations; otherwise, you are giving away free money to the government.
Claiming zakat in your tax return means you would either get a refund or pay less on your taxes depends on how your employer deduct the taxes from your paycheck. (if 0 dollar deduction from your paycheck, you most likely have to pay taxes, so better if you pay in advance like you are currently doing since you are receiving a refund) And you know right that the refund is the money they took out from your paycheck you earned from your hardwork and you get a refund because you have been paying too much extra taxes to the government. Thus, this is another story on taxes.