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Thanks to Drxx and CandleDave for the help regarding the 4 word phrase.

I was a tad concerned that, as I draw the grid by hand (albeit with a ruler), it wouldn't quite work but, amazingly, every cell required is touched by the two lines - plus I got to use my old technical drawing set again - so a win, win 😃

But, Brendan, didn’t you get an unwanted extra letter from the cell above the blank cell?

You're right, I see what you mean, it crosses the S in the SW corner but I'd put that down to my drawing of the grid - it's disappointing if that's not the case.

rad - When I enlarged the grid to redraw/check the lines I managed to hit all of (and only) those cells making up the phrase by placing the dot slightly south of the central position in the blank cell. My merest 'hit' was the first 'p' of the last word - it was just grazed.
I remember a similarly fine line (a spiral) having to be drawn in a Listener from years ago - that was pretty controversial too, and my effort was pretty hit and miss, so I'm happy to concede the point given my lack of precision in these matters. However, if the dot can be positioned to reveal the phrase then the preamble is accurate in stating, 'Solvers must place a dot...' (but I'm more than happy to backtrack from 'devious' to unfair).

Thanks, Drxx. As you pointed out earlier, the line going to the SE corner must pass precisely through a point where the printed gridlines cross, to avoid picking up unwanted letters. In the same way the other line must avoid the cells N and W of the blank cell. Thus the position of the dot is precisely determined as the point of intersection of these two lines, which is roughly two thirds of the way up from the bottom of the square and roughly a quarter of the way from left to right in the square. The mathematically exact ratios can be calculated by using coordinate geometry!

Thanks rad - I couldn't attempt to calculate the exact geometric point and I'm sure you're right about the exact point where the lines cross to avoid picking up surplus letters in the phrase (I'm assuming from your answer that it is possible to do so).

Hi

I've struggled with this but finally finished.

Have drawn the lines through the phrase but a bit confused by the preamble.

Are the other two lines drawn in on the entry grid?

Yes - four straight lines on the grid