The christening record for Heyltjen Jacobs L5Y9-5LH
gives her parents as Jan Jacobsz and Lambertjen Juriaens. Obviously, patronymics was NOT used, but it should have been. In 1634 the Dutch were using patronymics.
Yes - it's the INDEX that you want EDITED. And if the image does not reside on FamilySearch's servers, the INDEX cannot be edited.
The Index was likely imported from openarch.nl. That is often the case. Certainly there are many indexes on FS that come from other sites.
The image is not on FamilySearch but on the openarch.nl site. To edit an indexed record on familysearch, there must be an image on the familysearch site.
I don't want to edit the record. I believe it was indexed wrong. It should have been indexed using patronymics, but was instead indexed with the child being given the father's surname, NOT the patronymic. That makes the entire record incorrect.
I'm still not sure whether you're referring to the Family Tree record itself as "the christening record", or the earliest-dated source atttached to it, or something else.
You can certainly change the name of the child or the parents in the Tree, or add an Alternate Name for any of them, or delete the relationship if the sources contradict it, or add a custom fact as you've done already.
If you're asking how to complain about the data in the "record" at https://www.familysearch.org/ark:/61903/1:1:6ZTK-3FHH , in this case, because the data is maintained at an external site, you would need to report the concern to that site. If you go to https://www.openarch.nl/wfa:124DC339-CE83-482E-B083-8A9311A2E5AA and scroll down a bit, you should see "Report error in data" and "Add comment" buttons; I imagine you should use one of those options. (see screenshot below)
But even "openarch.nl" is only an "index"; the record there references https://www.westfriesarchief.nl/onderzoek/zoeken?mizig=236&miadt=136&miaet=54&micode=1702-09_5&minr=6915325&miview=ldt , which has images that I guess are the original christening register (or at least a written index oe extract made closer to the event). It might be helpful to link that directly as a source in the Tree, or reference it in a comment on any deletion you perform.