Question: Is it permitted to reprimand a fellow davener who is chatting during davening, even though it seems that the reprimand may make more noise than the chatting?

Answer: Yes. Davening is not the time for chatting.  It is very difficult for one to pray properly while his neighbor is chatting and he who chats during tefilah is in fact stealing from his neighbor the opportunity for prayer with proper kavanah.  We are in shul in order to pray to Hashem and not to chat with our neighbors. It would be appropriate to invite friends to a kiddush at home or donate a kiddush at the shul in order to facilitate chatting after shul.  In any case, if speaking during tefillah is absolutely necessary, it may be done at Kriyat HaTorah in between Aliyot, but never during Birchat HaTorah, Kriyat HaTorah and of course never during the Tefilah itself.