There is an interesting theoretical argument to be made (here is my pipe, take a puff). If you assume that the company is accruing cash for the dividend over the duration of the dividend period, the stock should be rising gradually and then dropping back by the dividend amount. Assume your spot is $100 and div is $1 - in a regular model, forward on the ex-div date will be $99 while in our "guaranteed dividends" model it's still $100, but it will be $101 the day prior to ex-date. If this is really true, puts priced in a regular model would be statistically overpriced - the fwd mis-pricing will be negligible if you delta hedge with stock, obviously.
There, now you can exhale - help yourself to some curry once the munchies start

). So you do not exercise the call when the value of the put is higher than the dividend... (I cut a few corners here, but otherwise I think it will too complicated).