Is a "Mut'ah" child born before its prohibition considered an illegitimate child? And was Mut'ah a selling of one's honor before it was abrogated?

The lineage of a child born from a temporary marriage (mut'ah) is established, whether the marriage occurred before or after its prohibition, provided the man believed it to be permissible. This is because, in a فساد (corrupt) marriage, the child's lineage is attributed to their father, and they inherit from each other by the consensus of Muslims. The mut'ah marriage was initially permissible and then forbidden.