Mrs Draper was happy to receive an email from her granddaughter on Tuesday, confirming she was safe and well, she said.
"I'm grateful she's safe."
"I said 'for god's sake be careful'- I didn't know she was on these marches."
She had not known her granddaughter to be especially political in the past, she said.
"She's obviously sort of started marching because everyone is upset. The whole country is so upset, the whole thing is really shocking ... "
Speaking to the Times-Age from Toronto, Canada, where she is spending the Thanksgiving holiday with family, Marie Draper said the peaceful protest was an attempt to highlight ongoing issues of oppression and inequality in the United States.
"For me it's not about this one particular case, it's about systemic racism and oppression.
"I believe that participating in a people's protest was one way to add my voice to a chorus of many, many others that are not being heard."
Other students from Washington University had been caught up in the Ferguson protests and several were pepper sprayed by police, she said.
It was important to show people were also protesting peacefully, Ms Draper said.
"We wanted to draw attention to this protest especially as the media has paid so much attention to the violent protests.
"I felt comfortable protesting because it's not just about this isolated case, it's about something much bigger than that ... police militarisation is one of the main issues people are protesting - [it] contributed to why there were so many bullets in Michael Brown's back."
Ms Draper said she would continue to raise awareness of racism and might participate in further protests, if more peaceful demonstrations were organised.