for file in $(find . -mindepth 1 -type f); do sed -i 's/remove\ this\ sentence/stringtoreplace/g' $file; done
Let's break it down.
$(find . -mindepth 1 -type f)
This will find every file starting in working directory, and return it as it's full path. Recursive in that you're searching a minimum depth of one (same directory) or more subdirs deep.
sed -i 's/remove\ this\ sentence/stringtoreplace/g'
-i modify file in-place
/g all occurrences of "remove this sentence" in lines as they're read.
And then there's the "for" loop, which iterates over the files.
Probably easier
Another way this can be done is by:
find . -mindepth 1 -type f -exec sed -i 's/remove\ this\ sentence/stringtoreplace/g' {} \;
...which is the same thing. Here, we're just using find to find the files and execute the sed replace in-place command on each one found.