This causes incorrect behavior. The STYLE tags should be removed along with the get_text method.
The origin of this problem is the behavior of the get_text method of the RadEditor control.

The following workaround can be used as a workaround for this issue. The implemented resolution is related to another logged bug - http://feedback.telerik.com/Project/108/Feedback/Details/119856

<telerik:RadEditor runat="server" ID="RadEditor1">
</telerik:RadEditor>

<script type="text/javascript">
	Telerik.Web.UI.RadEditor.prototype.get_text = function () {
		var $T = Telerik.Web.UI,
			modeEnum = $T.EditModes,
			oContent = "";

		if (this.get_mode() != modeEnum.Html) {
			var oArea = this.get_contentArea();
			if (oArea) {
				oContent = oArea.innerHTML;
				oContent = oContent.replace(/<br>/ig, "\r\n");
				oContent = oContent.replace(/<\/p>/gi, "\r\n");
				oContent = oContent.replace(/&nbsp;/gi, "\s");
				if (this.get_newLineMode() === $T.EditorNewLineModes.Div) {
					oContent = oContent.replace(/<\/div>/gi, "\r\n");
				}

				oContent = oContent.replace(/\s*<div[^>]*style="display:none;"[^>]*>[^>]*>\s*/gi, "");
				oContent = oContent.replace(/\s*<style[^>]*>[^>]*>\s*/gi, " ");

				oContent = oContent.replace(/<\/?[^>]*>/ig, "");
				oContent = oContent.replace(/<!--(.|\s)*?-->/gi, "");
			}
		}
		else {
			oContent = this._getTextArea().value;
			oContent = oContent.replace(/\s*<style[^>]*>[^>]*>\s*/gi, " ");
			oContent = oContent.replace(/<\/?[^>]*>/ig, "");
		}
		return oContent;
	};
</script>