The phrase "a section of their" is correct and usable in written English.
It can be used when referring to a specific part or segment belonging to a group or entity.
Example: "The report includes a section of their findings on climate change."
Alternatives: "a part of their" or "a segment of their".
There's a section of their opinion devoted to that.
The winner was allowed to paint a section of their opponent's campus a color of their choice.
Italy: Lazio director Igli Tare, on why a section of their fans abused Bayer Leverkusen's black players.
Uefa sanctioned fans' racist behaviour by closing a section of their stadium at a Champions League play-off last season.
Indeed, they devoted a section of their letter specifically to their aspiration "to make Google an institution that makes the world a better place".
Many schools now have a section of their behaviour management systems on homophobia, but I have only once encountered a section that specifically noted transphobia.
Wong et al. have now genetically engineered mice to lack a section of one of their copies of chromosome 7 that is often missing in patients with MDS.
Shortly thereafter, they released a big chunk of webOS 2.0 to a small section of their development community as part of a Beta program.
When clicked, it saves a link to the article to a "Saved" section of their Timeline.
Los Angeles basically turned a whole section of their downtown area into a magnet for homeless people by building all of their social services and health facilities for the poor in the same neighborhood.
In their silly desperation to paint Labour as a bunch of commies, they find themselves talking to a small section of their core electorate, while Labour speaks for the broad majority of the British public.
