The borders can be removed by combing a zero line width with zero tile padding.
Here's an example that Plotly has put on their site with the standard borders.
# example from at https://plotly.com/r/treemaps/
plot_ly(
type="treemap",
labels=c("Eve", "Cain", "Seth", "Enos", "Noam", "Abel", "Awan", "Enoch", "Azura"),
parents=c("", "Eve", "Eve", "Seth", "Seth", "Eve", "Eve", "Awan", "Eve")
)

Here is the same plot without borders.
# no borders
plot_ly(
type="treemap",
labels=c("Eve", "Cain", "Seth", "Enos", "Noam", "Abel", "Awan", "Enoch", "Azura"),
parents=c("", "Eve", "Eve", "Seth", "Seth", "Eve", "Eve", "Awan", "Eve"),
marker = list(line = list(width = 0)),
tiling = list(pad = 0))
