Is that the actual email that you've copied-and-pasted, or have you typed it in (there are a few typos in it, which if it was a pasted copy I wouldn't expect to be in a genuine Apple email) ? If that is the actual text then it look like a phishing attempt to get her details.
Has she checked the purchase history on her account ? If she logs into her account on her computer's iTunes via the Store > View Account menu option, she should then see a Purchase History section with a 'see all' link to the right of it, if she clicks on that she should then see a list of her account's purchases (the most recent purchase is above the list).
If it shows there then she can contact iTunes Support via this page : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page, then Purchases, Billing & Redemption
She should also change her account's password e.g. by logging into it via the Store > View Account menu option on a computer's iTunes, tapping on the id in Settings > iTunes & App Store on an iOS device, or via http://appleid.apple.com
That's ok, I was just checking - there are various phishing emails going around trying to get you to click on links in them which then take you to a non-Apple site and ask for your login and payment details, though they tend not to be personalised emails (e.g. they have something like 'Dear customer').
If she hasn't already done so then she should :
- check her account's purchase history
- change her password
- contact iTunes support
When a purchase is made from a computer or device for the first time then the account's security questions should be asked for, or 2-step verification is required to verify the purchase. Do you know if she has security questions set on her account or is using 2-step verification ?
For security questions she can set/change them by logging into http://appleid.apple.com and selecting the Password & Security section on there
About security questions : http://support.apple.com/kb/HT5665
Rescue email address : http://support.apple.com/kb/HT5620
Or she could use 2-step verification if it's available in your/her country : http://support.apple.com/kb/HT5570
You can't delete an account, all you can do is remove personal info from an account and stop using it.
If it's not her account then it's possible that somebody has mistakenly added the email address as a rescue or alternate email address on their own account - in which case there is probably not much that your sister can do, though she can try contacting iTunes Support (but I don't think that they will be able to do anything) : http://www.apple.com/support/itunes/contact/