You'll need to read everything in the file, store it somewhere (a string only if you know the file will never go over 4096 bytes, otherwise you'll need to use another file), delete the line you're looking for, than rewrite it.
For example, something like this
Using a string
%file = new FileObject();
%file.openForRead("base/myFile.txt");
while(!%file.isEoF())
%wholeFile = %wholeFile NL %file.readLine();
%file.close();
strReplace(%wholeFile,"stuff to delete\n","");
%file.openForWrite("base/myFile.txt");
%file.writeLine(%wholeFile);
%file.close();
%file.delete();
Using another file
fileCopy("base/myFile.txt","base/myFileBuffer.txt");
%file = new FileObject();
%file.openForWrite("base/myFile.txt");
%fileBuffer = new FileObject();
%fileBuffer.openForRead("base/myFileBuffer.txt");
while(!%fileBuffer.isEoF())
{
%line = %fileBuffer.readLine();
if(%line !$= "stuff to delete")
%file.writeLine(%line);
}
%file.close();
%file.delete();
%fileBuffer.close();
%fileBuffer.delete();
fileDelete("base/myFileBuffer.txt");
Both untested