Answer by Professional Japanese Teacher
I am very sorry for your loss. Your father must be a wonderful man to have many former overseas students coming for his funeral.
“Thank you” is “arigatoo” or “arigatoogozaimasu” in Japanese. In Japanese language, the level of politeness differs according to the relationship with the target audience.
For people who are close to us, we use “arigatoo”. For business associates or older people, we use the more polite version “arigatoogozaimasu”.
However, even for people who are close to us, we use “arigatoogozaimasu” especially in formal situations or situations where we wish to reassert ourselves.
This makes the language more refined or sophisticated. The person(s) you are writing to is your former host family. If you wish to show a sense of familiarity, you can say “kitekurete arigatoo”.
If you wish to express your thanks again formally even for close friends, you can say “kitekurete arigatoogozaimashita”.
“Gozaimashita” means past tense. We use “gozaimashita” to show thanks for past actions.