There are two types of almond paste typically available in grocery stores. An almond paste with a higher percentage of almonds (between 45 and 52%) is less sweet and works better for recipes, like this one, where the paste needs to be creamed or puréed.
If you would like to omit the peaches in this recipe, you can replace the peach syrup with the same quantity of simple syrup flavoured with vanilla, to taste.