The boys have found a rope hanging from a branch of a tree across the river. They refer to it as a Tarza ie a Tarzan rope.
The boys in the story are more likely to have come across Tarzan from the screen rather than off the page. Tarzan films started as early as 1918, in the silent era. The actor who played Tarzan in the period covered by the stories was Gordon Scott (1955-1960) and yet, mainly because of Saturday morning TV repeats, the boys would have been most familiar with the most popular Tarzan of all time, Johnny Weismuller, the five-times Gold medal swimming champion, who played Tarzan from 1932 to 1949.
Here is Johnny Weismuller's famous Tarzan cry.
And here is the famous meeting between Tarzan and Jane, with the 'Me Tarzan, you Jane' exchange adapted by Palmer in the quote above.