Praise be to Allah.
Women should cover their faces in front of non-mahram men, because of a great deal of evidence that has been quoted in the answer to question no. 11774. Based on this, she should not be smiling in this manner in the first place.
A great deal of shar’i evidence indicates that it is not allowed to do that which may cause men to be tempted by women and vice versa, such as shaking hands, being alone with a member of the opposite sex, speaking in a soft voice, a woman going out wearing perfume so that its fragrance may be smelt, a man looking at women and a woman looking at men if that is with desire.
See the answer to question no. 84089 for more information on the evidence concerning that.
For a woman to smile at a man to be kind to them for the purpose referred to in the question implies that each of them is looking at the other, and that is forbidden because Allaah says (interpretation of the meaning):
“Tell the believing men to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts). That is purer for them. Verily, Allaah is All‑Aware of what they do.
31. And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts) and not to show off their adornment except only that which is apparent (like both eyes for necessity to see the way, or outer palms of hands or one eye or dress like veil, gloves, headcover, apron), and to draw their veils all over Juyoobihinna (i.e. their bodies, faces, necks and bosoms) and not to reveal their adornment except to their husbands, or their fathers, or their husband’s fathers, or their sons, or their husband’s sons, or their brothers or their brother’s sons, or their sister’s sons, or their (Muslim) women (i.e. their sisters in Islam), or the (female) slaves whom their right hands possess, or old male servants who lack vigour, or small children who have no sense of feminine sex. And let them not stamp their feet so as to reveal what they hide of their adornment. And all of you beg Allaah to forgive you all, O believers, that you may be successful”
This smiling may have an effect on the heart that is not less than the effect of soft speech, and it may lead to the fitnah (temptation) that Allaah has warned against when He said (interpretation of the meaning):
“O wives of the Prophet! You are not like any other women. If you keep your duty (to Allaah), then be not soft in speech, lest he in whose heart is a disease (of hypocrisy, or evil desire for adultery) should be moved with desire, but speak in an honourable manner”
The Standing Committee for Issuing Fatwas was asked: What is the ruling on a woman who smiles in front of a non-mahram man, but without showing her teeth and without making any sound?
It is haraam for a woman to uncover her face or to smile at a non-mahram man, because of the evil to which that leads. And Allaah is the Source of strength. May Allaah send blessing and peace upon our Prophet Muhammad and his family and companions. End quote.
The Standing Committee for Academic Research and Issuing Fatwas.
‘Abd al-‘Azeez ibn ‘Abd-Allaah ibn Baaz, ‘Abd al-Razzaaq ‘Afeefi, ‘Abd-Allaah ibn Ghadyaan.
End quote from Fataawa al-Lajnah al-Daa’imah (17/25).
With regard to the Muslims from other countries whom you mention, the Muslims should honour them, make them feel welcome and take care of them, without doing anything that is haraam. Men should take care of men and women should take care of women. You will find many Muslim women who need your care and kind treatment.
May Allaah increase us and you in guidance.
And Allaah knows best.