Parents never want to be a burden on the kids.
Frame assessment as a way to stay independent for longer
Convince older adults that assessment identifies issues that keep them independent for longer. This helps the conversation go from "there is a problem" to "let's figure out how to keep you well."
Remove points of friction
Travel, appointments, and queues often get in the way. Tell them that the assessment happens in the comfort of their own home, and that they don't need to arrange anything.
Their primary care physician stays the same
Assure them that they will not have to change any primary care or specialist doctor they are already seeing. This is an additional layer of support that a five-minute appointment with the doctor sometimes cannot provide.
Give yourself peace of mind as their child
Tell them this will give you, their child, peace of mind, knowing there is a pair of medically trained eyes seeing them regularly.
Lastly, and most importantly, sometimes a few gentle conversations are needed before they are convinced. So be patient.