Can my last employer ask which company am joining next?

Hello, I had put down my papers in month of Feb and got relieved from duty on 30th April,2020 from Company ABC. I have joining new company XYZ in first week of May, 2020. Now, during the background verification by new employer's vendor, they sent the email to my last employer ABC asking few details to which they replied that they need details like which company am joining and whats the location. I came to know about this from my new company's vendor for which they needed my consent before disclosing the details to my last employer. Before giving the details, i called my last company HR and asked them why they need those details and they said its company policy. After lot of argument i have surrendered and had to give the consent to the vendor to disclose these details. So my question, is it legally correct for my last employer to ask which company am joining ?