what part of speech is grammatically incorrect When they saw that there dog had been eaten by the mad cow were more than a little upset?

The grammatically incorrect part of speech is the noun "dog". It should be possessive: "their dog".

Here's why:

* Possessive Pronouns: "Their" is a possessive pronoun, indicating that the dog belongs to "they".

* Possessive Adjectives: "Their" is also functioning as a possessive adjective, modifying the noun "dog".

The corrected sentence would be:

> When they saw that their dog had been eaten by the mad cow, they were more than a little upset.