Although there is sometimes a halachic basis for permitting mikveh immersion with items intended for beautification that are not meant to be removed, hair extensions are generally considered a chatzitzah.
The laws of chafifah and chatzitzah are especially stringent when it comes to hair. Women do not immerse with knots or braids in the hair, since they block water from reaching each strand of hair. Foreign bodies tightly attached to the hair, such as tape or adhesive, present even greater halachic difficulty.
We strongly suggest not using tape-in extensions and, if possible, pursuing a more easily removable alternative such as clip-ins.
If a woman very strongly desires extensions and plans to have them in place for at least six months, there is room to accept an immersion with them. However, to the best of our knowledge, tape-in extensions do not last for that long.
Please feel free to get back to us with any further questions.