Is there a tax on hospital invoices which international patients can get refunded?

This is a question, that has been posed a number of times. The answer is: Generally not.
The fact is: For normal medical treatment there is a general exemption from the VAT (Value added tax), for non-profit hospitals (the vast majority of hospitals) as well as for private clinics. Medical services, at least as long as they are medically necessary, can be invoiced without VAT; consequently there is nothing to get refunded when the patient returns home.
By the way: The same applies for doctor's fees: Doctors do not qualify for VAT invoicing for medical services they provide.
Only in such cases, where no medical need whatsoever can be shown, for example plastic surgery for purely aesthetic reasons, this service will be considered to be simply commercial, and the VAT has to be added on the bill. And even in such cases, if the hospital normally has only medical treatment patients, the VAT will often be forgotten by the administration (how should they know, that there are no medical reasons for the treatment in this specific case?)
But of course, if a private clinic has specialized on such operations, or if a doctor also sells goods (like a special machine or drug) they will be in the focus of tax authorities and will add the VAT routinely.
But that will be a rare exception.