Invitation Letter Thank You
Whether you have received an invitation letter to a wedding, a business function, or a lunch party, it is common courtesy to send a thank you letter in response either to confirm you will be attending or after the event.
Responding to a social invitation letter is more common; it is not needed at all for an invitation letter for a visa. Again, it is not mandatory in any case but is seen more as a polite gesture to thank the host for what they had done.
Thank You Letter to RSVP
You would usually send a reply to confirm attendance at an event by whatever form has been mentioned at the end of the invitation letter. In your response, it is good to simply mention your gratitude for being invited and that you look forward to attending the event. Your reply can remain brief, it does not have to be formally written and it is up to you what method you want to use: verbal, email or letter.
Thank You Letter After Event
This is also an optional follow-up to an invitation letter that you can choose to do or not. It is seen as a kind and polite gesture to make that shows your appreciation towards the host of the function. Depending on the purpose of the event will result in how formal/informal you should be in your invitation letter thank you. You may choose whether to send a gift in addition or not, for example if someone has hosted an event on behalf of you or your company, this is a good idea.
Have a look at these invitation letter samples to guide you.