Can you help me with English please?

"Pestered" is a verb, the past tense of "pester".

"Eventually" is an adverb, modifying the verb "bundled".

"Bundled is a verb, the past tense of "bundle".

The dictionary is your friend.

I was going to encourage you to look them up, but after I saw the poor responses you have received from others, I thought I'd better help you. Many words mean more than one thing.

Ravi has given you a pretty good definition of "pestered".

"Pester" means to repeatedly bother somebody in a relatively minor, yet annoying way.

However, his other definitions could be better.

Eventually" means "after some time", such as after being delayed, or after overcoming a series of problems, or a after prolonged effort.

example: Mary dieted for 12 months, but eventually lost 100 pounds.

example: Tom read the passage 5 times before he eventually understood its meaning.

In this case, it means the grandfather allowed Heidi to pester him for some time -- he put up with it for quite a while -- before he took action.

"Bundle" also means to "join together in one package" or to "wrap up".

example: Mary bundled the book, hat, and map for shipment

example (in this passage): Grandfather bundled Heidi up in a blanket. He wrapped her up, to make her feel snug and secure (but also, hopefully, to calm her, and to restrain her a bit, so that she would stop pestering him).

"Oh come on, Grandpa, please wrap me up in this blanket. Come on, I 've been asking you for an hour and you won't do it. When are you going to wrap me up? How many times do I have to ask you? I'm going to hold my breath until I turn blue if you don't wrap me up."

"Oh, phooey! Here, if it will shut you up, I'll put this blanket around you even if I think it's a stupid idea."

Grandpa takes blanket and folds it around pesky kid.

pestered; past participle: pestered

trouble or annoy (someone) with frequent or persistent requests or interruptions.

Eventually- lastly

bundled- to send away hurriedly or unceremoniously (usually followed by off, out, etc.):

They bundled her off to the country.

Invest in a thesaurus.