The right answer is "he passes by her grave everyday".
The irony in this case is that the dog speaks in the text that it passes by that place every day, soon after it says that it forgot that that is the lady's tomb, but if the dog goes there every day it knows the place very well, so it knows where the graves are and who owns them.
It is important to point out that irony is a figure through which the opposite is said of what one wants to imply.