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The following is one of three opinions among the scholars.
You do not have to respond to the walima invitation. It is a Sunnah to respond. It is not waajib. This is the opinion of the masses of the Hanafi and Shaafi'i. It is a saying amongst the Hanaabilah. Ibn Taymiyyah chose this opinion.
Walima involves eating food and taking possession of maal. No one is required to take possession of the maal of someone else without choice. Take Zakaah as an example. The one who is given Zakaah is not required to take it. Such is the case with all forms of Zakaah despite the fact that they are obligatory. Thus, it is more befitting in the case of things other than Zakaah like the walima.
Kuwaiti Encyclopedia of fiQh
Volume 45 Page 236