"When they say reduced, they mean by being taxed not the actual check." No they mean your actual monthly checks will be reduced. They somehow know.
SS says.... https://www.ssa.gov/benefits/retirement/planner/whileworking.html
If your earnings will be more than the limit for the year and you will receive retirement benefits for part of the year, we have a special rule that applies to earnings for 1 year. The special rule lets us pay a full Social Security benefit for any whole month we consider you retired, regardless of your yearly earnings.
And see this https://www.ssa.gov/benefits/retirement/planner/rule.html
Neither of those links say anything about the taxability of your SS. Just how much they will pay you regardless of the tax on it. You can have tax withholding taken out or not to cover the tax.
