Hope someone can help here.....

I have stupidly lost my annual Oystercard.

Been on to the website and reported it lost and told a new one will be with
me within 5 days.

In the meantime I am using another pre-pay oyster. Is there anyway of
getting some money back for the period when I have had to pay for travel ?

Before Oyster I would have been able to go to my "home" ticket office and
get a duplicate ticket issued. Could not find anything on "Ask Oyster".