If my wife has over contributed to her RRSPs by $2300 with the one time allowance of $2000 would she only be penalized on the $300 and should she withdraw that amount?

Your wife will be penalized for 1% of the amount exceeding $2000 that is excess contribution.  

http://www.cra-arc.gc.ca/tx/ndvdls/tpcs/rrsp-reer/cntrbtng/xcss-eng.html

As to withdrawing the excess it would help reduce the penalty you will pay.  You also need to file the following return, there will be an additional penalty of 5% as the deadline was 90 days after the end of the calendar year.

http://www.cra-arc.gc.ca/E/pbg/tf/t1-ovp/README.html