What is the word for using someone's hospitality unashamedly?

This so-called "guest" is presuming on his hapless victim host. In other forms, this person is said to be, presuming on someone's generosity, or just presumptuous.

Among the definitions of presume at dictonary.com you will find

to act or proceed with unwarrantable or impertinent boldness

Also, among the Yiddish words we presume to use in English is Schnorrer, which I once heard described as "someone who barges into your house and throws open the refrigerator".

A common term is freeloader

A person who takes advantage of others' generosity without giving anything in return.

Oxford Dictionaries Online

Freeload is similarly defined in Merriam-Webster

to impose upon another's generosity or hospitality without sharing in the cost or responsibility involved

Another informal term is sponge

informal [no object] Obtain or accept money or food from other people without doing or intending to do anything in return.

they found they could earn a perfectly good living by sponging off others

Oxford Dictionaries Online

... the important thing here is that the guest knows that they shouldn't do that, but they just don't care.

It's not a single word, but it's important to note that it's better to use the idiom overstay (outstay) one's welcome which means:

to stay at a place for longer than people want

[Macmillan Online Dictionary]

The guest in context is scrounging for food.

ODO:

scrounge VERB
[WITH OBJECT]
informal
1 Seek to obtain (something, typically food or money) at the expense or through the generosity of others or by stealth:
‘he had managed to scrounge a free meal’

‘You spend your benefit money on drugs and then you come round here scrounging for free food.’

Also, mooching.

ODO:

mooch VERB
informal

2 North American [with object] Ask for or obtain (something) without paying for it:
‘a bunch of your friends will show up, mooching food’
[no object] ‘I'm mooching off you all the time’

‘They are nice in every way, except for the fact that they always try to mooch food from us.’
‘He goes around the cafeteria and floats from table to table, talking with everyone and mooching off them at the same time so he doesn't have to pay for lunch.’