Grammar my dear!
You're no longer talking, but writing.
their:
ownership. It is their book.
there: indicates
location (etc), Over there, not here.
they're: short for
they are.
In the short text, you have nice examples of all three:
- Their work requires them to travel every couple of months,... OK
- ..., so their was loud music playing... NOT OK, should be there.
- “Fuck their loud” NOT OK, should be “Fuck. They're loud”
See Merriam-Webster