This website is crediting openstreetmap by linking to the openstreetmap page.
I said to the owner that I believe this is incorrect as the license says that you need to make it clear that the data is under ODbL the owner claims that this is optional and linking to the normal page is enough due to it saying “you may link to this copyright page” is this correct?
See Licence/Attribution Guidelines - OpenStreetMap Foundation
Attribution must also make it clear that the data is available under the Open Database License. This may be done by making the text “OpenStreetMap” a link to OpenStreetMap, which has information about OpenStreetMap’s data sources (which OpenStreetMap needs to credit) as well as the ODbL.
Note that this site has quite good attribution - it does not disappear on smaller screens based on quick test.
I would recommend thanking them for proper attribution and give them link to this instructions so they know that it is done in a proper way.
(and thanks for caring about attribution! though maybe being a tiny little bit less aggressive would be a good idea - but either way posting here question on forum is much better than being 100% sure about being right)
(in ideal world attribution would make clear what is credited for what but that is so high standard…)