I know that the rule of ה״א התימה is that it usually takes a הֲ unless it precedes a שוא, such as here in הַכְזוֹנָה, where it then just takes a הַ and the following letter doesn't have a דגש in order to different it from the ה״א הידיעה, which does have a דגש. The issue, though, is from a similar word we have in פרשת תולדות כז:לח. On the words הברכה אחת, which is a question, רש״י comments ה״א זו משמשת לשון תמיה, and brings three examples of words that are questions, but have a הַ rather than a הֲ. However, in all of the examples there is a דגש in the letter after the ה״א when there usually shouldn't be.
ראב״ע brings in his ספר מאזנים that a דגש is allowed after a ה״א התימה that precedes a שוא (making the ה״א punctuated as הֵ) if the letter with the שוא is an אות השמוש or אות השורש. That explains the why there is a דגש in the examples רש״י brings. However, according to that, the בי״ת in הברכה and the כ״ף in הכזונה should both have a דגש! In ספר צחות (also from ראב״ע), he says that there is no דגש in the בי״ת of הברכה so that there is no confusion that it might be a ה״א הידיעה. A similar idea is found in the גר״א's דקדוק ופירוש על התורה (also brought in ספר לשון חיים) that we can use a דגש after a ה״א התימה punctuated as הַ when there is no issue of confusion.
Perhaps you could apply the same logic here that we don't want to risk confusion. However, I haven't seen that brought down in any of the ספרים I've looked at that discuss the rules and exceptions...
