On p.52 of the handbook, it says this about "sporadic or non-recurring income":
"Certain forms of income that are sporadic and non-recurring are not considered when calculating maximum household income as they are considered temporary in nature. Examples of sporadic or non-recurring income include one-time gifts or lump-sum inheritance payments. All sources of income must be disclosed, but such non-recurring income may be excluded from the income calculation."
You said the $500 was recurring, but it's also clear it was meant to be temporary and was more in the nature of a gift. If they ask (maybe they won't), I think you just explain it honestly as you did here and they might still decide that it doesn't count as income for these purposes.
https://www1.nyc.gov/assets/hpd/down...g-handbook.pdf