Other than company logo, there cannot be any other logo on the visiting card. Occasionally companies also print logo of some certifying agency or agency that does some accreditation. But then this decision has to be taken at the management level.
If Finance Head may print his CA logo on his personal card and not on official one.
Till he works for the company the business card will have only company logo.
As a HR representative you should escalate to management and also to explain the issues expected in case accepts.
HR & Labour Law advisor
A CA working for a CA firm can use the CA logo on his visiting card.
However, a company can not put CA Logo on any visiting card of the company.
You may check the CA institute website for details of where the logo can be used and where it cant.