The phrase all right, you heard a seal bark is used as the title of this article, published in The Detroit Free Press (Detroit, Michigan) of Tuesday 26^th August 1958:

All Right, You Heard a Seal Bark!

Two five-foot seals that had starring roles at the Police Field Day at Briggs Stadium Sunday had even bigger roles outside the ball park Monday night.
The seals, apparently abandoned, were barking noisily at the rear of 2251 National.
They were in a water tank inside a big white semi-trailer with no markings.
Where their trainer went after he was paid for their appearance is something that every policeman in Detroit was asked to determine by Supt. Louis J. Berg.
Lt. Edward Naisbitt, of Vernor Station, said the seals were hungry.
He had the seals towed to the dog pound and arranged for a 25-pound fish banquet.

The phrase all right, you heard a seal bark refers to the caption to a drawing by the U.S. cartoonist and author James Thurber (1894-1961), originally published in The New Yorker (New York City, N.Y.) of Saturday 30^th January 1932. This is the drawing, as reprinted in the Minneapolis Morning Tribune (Minneapolis, Minnesota) of Sunday 10^th October 1948:

“All right, have it your own way—you heard a seal bark.”

O. O. McIntyre (1884-1938) gave the following details in his column New York Day by Day, published in many U.S. newspapers in December 1932—for example in The Waco News-Tribune (Waco, Texas) of Friday the 9^th:

James Thurber draws those childishly amateur but hilarious sketches for the New Yorker. His high in cock-eyed absurdity revealed a seal peering from the head-board of a bed occupied by a dispirited husband and his domineering wife. The catch-line read: “All right, have it your own way—you heard a seal bark?” Thurber is a new-comer who comes nearest usurping Peter Arno’s ¹ throne.

¹ Peter Arno (Curtis Arnoux Peters, Jr – 1904-1968) was a U.S. cartoonist—cf. origin of ‘back to the drawing board’.

This is an interesting review of The Seal in the Bedroom and Other Predicaments (New York: Harper and Brothers, 1932), by James Thurber—written by ‘B. B.’, this review was published in The Courier-Journal (Louisville, Kentucky) of Sunday 18^th December 1932:

You can tell pretty well whether or not this book will amuse you by giving yourself a simple test. Pick it up, look at the first drawing, and see how you are affected by the sight of a pair of monolithic people sprawled in bed, with a seal brooding over them from a head-board, and the beaten-down husband saying to his shrew, “All right, have it your way—you heard a seal bark.” If you laugh, get out your $2 quickly, lie down somewhere so that you cannot fall on your face when you get really amused, and start turning the pages.
If carefully analyzed, these drawings could not be as funny as they actually are. It would even be possible to work yourself into a state of black depression over too minute a study of these wayward pen-strokes, but Thurber’s people are most uproarious when they are most bedraggled. Some of these drawings look like the sketches you might find on the walls of old abandoned telephone booths. Others look like what you yourself drew in your Fifth Grade B days when Miss Pritchett was not looking. Still others might have been found crumpled up under the settee in a psychoanalyst’s waiting-room. They are the phantasmagoria of a modern kind, the genii that come out of gin bottles. The people who wabble through these pages, waving their fins at you, are not like anything you ever saw before, but once you have beheld them, you keep seeing supposedly human beings who have those faces and those stomachs.
The New Yorker has to be thankful for introducing Thurber to the American public. The imagination staggers at the thought that he may be at times his own model when he draws. Perhaps that dejected penguin—?

Published in The Morning News (Wilmington, Delaware) of Monday 12^th July 1982, this cartoon by Jack Jurden is inspired by James Thurber’s The Seal in the Bedroom; “religious and charitable institutions” is written on the blanket and footboard, “flat rate income tax” on the seal perched on the headboard, and the caption is:

All Right, Have It Your Way—You Heard A Seal Bark

The explanation of this cartoon is found in an article published in the same newspaper, The Morning News (Wilmington, Delaware), on Thursday 8^th July 1982; President Ronald Reagan ², said this article, wanted to introduce the flat-rate income tax:

Supporters of the flat-rate income tax call it simple, fair and potentially a method of increasing revenues merely by making it easier for the Internal Revenue Service to find and prosecute tax cheats.
The idea is to apply a single tax rate—10 percent or 20 percent—to all Americans who pay income tax, and to eliminate most if not all currently allowable tax deductions.
Religious and charitable institutions are opposed on the grounds that this would shut off many contributions that are now tax-deductible. President Reagan reassuringly says that would not be the case. He bases his optimism only on the observation that “people were contributing to charities long before there was a system of taxation.”

² The Republican statesman Ronald Wilson Reagan (1911-2004) was the 40^th President of the USA from 1981 to 1989.