The style of the event links on the calendar is .zoomTip

If you want to differentiate it from looking like a normal link according to your joomla template, you can add the .zoomTip to the style parameter on the module configuration page and construct the style as you wish.

For example

.zoomTip {background-color:#FFBE5B;}

will make the background of the link pink.

In case you want to configure the tooltip or the entire calendar's style, the elements .D-tip , D-title and .D-text control the appearance of the tooltip's background, title, text areas respectively, while class .D_Calendar controls the appearance of the body of the calendar. Please note that those classes already exist inside the style parameter on the configuration page, so you only have to change them to whatever you want, even to transparent.