She thinks that some impurity got onto her clothes; Are her Hajj and prayer invalidated by that?

Firstly: 

The impurity that got onto your clothes does not affect the
validity of Hajj in sha Allah, because the essential parts of Hajj without
which it is not complete are four: ihraam, which is the intention to do
Hajj; Tawaaf al-Ifaadah; saa‘i between al-Safa and al-Marwah; and the
standing in ‘Arafah. In the case of these four essential parts, it is not
stipulated that one’s garment should be clean and pure, apart from what some
scholars mentioned with regard to tawaaf, and that only applies in the case
of one who is certain that there is some impurity (najaasah) on his body or
garment. But in the case of any uncertainty, tawaaf is valid. 

Secondly: 

The Muslim does not have to change his clothes in the event
that any impurity gets on to them. It is sufficient for him to remove that
impurity with whatever means are available to him. And he should remember
that the Shaytaan may open the door to waswasah (whispers) which may have no
end, so he may whisper to him that the impurity has not been removed and
that the garment has not been purified, hence his prayer is not valid, and
so on, to fill him with worry, distress and anxiety until his entire life is
ruined. 

Islam seeks to prevent this from happening to the Muslim in
the first place, so it instructs him to dispel doubt and not pay any
attention to it. 

It was narrated from ‘Abd-Allah ibn Zayd that a man
complained to the Messenger of Allah (blessings and peace of Allah be upon
him) that he thought that something had happened when he was praying, and he
said: “Do not stop until you hear a sound or notice a smell.”

Narrated by al-Bukhaari (137) and Muslim (361). 

This hadeeth is the basis for the principle that “certainty
is not dispelled except by an equal certainty.” The basic principle with
regard to one who is praying is that he is taahir (pure) and should not stop
praying unless he is certain that his wudoo’ is broken. 

The same applies in the case of the sister who asked the
question: the basic principle with regard to her garment is that it was
still pure (taahir), because she was not certain that there was any impurity
on it. She says, “I feel that my clothes got dirty.” In that case, she is
not certain that there was any impurity on her clothes. 

Based on that, if the Muslim is certain that there is any
impurity on his body or garment, what he has to do is remove it, and it is
not permissible for him to pray in that garment before he removes the
impurity. If he is uncertain as to whether there is any impurity, then he
should not pay any attention to it, because the basic principle is that
there is no impurity and he does not have to do anything further if he
prayed or circumambulated the Ka‘bah when this was the case. 

Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have
mercy on him) said: 

Islam – praise be to Allah – is complete in all aspects and
is suited to the nature of man as Allah created him. It is a religion of
ease and in fact came to keep man away from confusion, whispers and thoughts
for which there is no basis. Based on that, the basic principle with regard
to the individual and his garments is that they are pure, unless there is
certainty that there is any impurity on his body or garments. This basic
principle is attested to in the words of the Prophet (blessings and peace of
Allah be upon him) when a man complained to him that he thought that he
found something whilst praying – referring to minor impurity. The Prophet
(blessings and peace of Allah be upon him) said: “Do not stop until you hear
a sound or notice a smell.”. So the basic principle is that things remain as
they are. 

With regard to clothes that people wear when entering
bathrooms and relieving themselves – as mentioned in question – if they get
damp, who can be certain that this dampness is caused by an impurity such as
urine or water tainted with stools and the like? If we are not certain about
that, then the basic principle is that things remain pure (taahir). It is
true that he may think it most likely the case that it has been contaminated
with something impure, but so long as we are not certain of that, then the
basic principle is that it remains pure. 

So in answer to this question, we say: if they are not
certain that their garments have got anything impure on them, then the basic
principle is that they remain pure and they do not have to wash their
garments. They can pray in them with no problem. And Allah knows best. End
quote. 

Majmoo‘ Fataawa Ibn ‘Uthaymeen
(11/question number 23)  

And Allah knows best.