Not sure if there is a proper objection handling there, so I would love to hear it.
I get cold calls on my private number all the time and don't see the issue, a cold call is a cold call, it might be B2C and I could be selling them insurance and not B2B, so I don't see the problem there, apart from them brushing you off. This is typical in the US. As if cold calls are reserved only for their business number, lol, I can't process that, since we're calling them during business hours.