Communicating with the Matlab folks, they clarified that it implicitly uses a $100 face value for the bond. The conversion ratio needs to be adjusted accordingly.
The dividend yield has been specified as well in the last two lines of the invocation.
% CbMatrix = cbprice(RiskFreeRate, StaticSpread, Sigma, Price, ...
% ConvRatio, ...
% NumSteps, IssueDate, Settle, Maturity, CouponRate, ...)
>> CbMatrix = cbprice(0.03, 0.00575, 0.236, 24.49, ...
34.24 * 100 / 1000, ... % changed here
100, '30-Mar-2006', '20-Jun-2013', '15-Dec-2035', 0.0295, ...
'DividendType', 2, ...
'DividendInfo', [datenum('20-Jun-2013') 0.0453]);
>> CbMatrix(1,1)
ans =
107.3614