Jvector Map add/remove function shorten code
You are looking to remove the copy pasted code, to make it more DRY.

Beyond that, it seems that really whether you getID or removeGetID, you set a number of ID's and then update mapObject. Furthermore, it seems that you do not need to update mapObject within the loop, which is slow.

I would counter-propose

var helpfullyNamedConstant1 = '#3e9d01';
var helpfullyNamedConstant2 = '#128da7';

function setContinentCodes(continentId, continentCodesValue ){
    jQuery.each(mapObject.mapData.paths, function(i, val) {
            if (val.continent == continentId){
                continentCodes[i] = continentCodesValue ;
            }
    });
    mapObject.series.regions[0].setValues(continentCodes);
}

jQuery('.continentLink').hover(function(e) {
    setContinentCodes(this.id, helpfullyNamedConstant1);
}, function(){
    setContinentCodes(this.id, helpfullyNamedConstant2);
});