“Intruder window” is an old joke for “in troo der window” or “in through the window.” The joke (“he climbed intruder window”) might have originated in the New York City humor magazine The Judge in 1925.
   
“Bill got locked out of his house last night, but he climbed intruder window” was printed in the San Luis Obispo (CA) Daily Telegram on May 21, 1929. “Hmmm, how does that one go about the crook who got inside the house by climbing intruder window?” was printed in the book The Best of American Jewish Humor (1976) by Henry D. Spalding. “How did the burglar get into the house? Intruder window” was printed in the Chicago (IL) Tribune on November 22, 1994.
 
         
Google Books
The Judge
Volume 88, Issue 2269
1925
Pg. 27:
Her Father j^.s^-* threw him out but V ** he climbed intruder window. (Google Books is illegible.—ed.)
 
21 May 1929, San Luis Obispo (CA) Daily Telegram, “Trib -o- Grams,” pg. 4, col. 1:
“INTRUDER”
Bill got locked out of his house last night, but he climbed intruder window.
 
15 February 1932,  San Luis Obispo (CA) Daily Telegram, “Trib -o- Grams,” pg. 4, col. 3:
INTRUDER
“The burglar climbed intruder window.”
     
Google Books
The Best of American Jewish Humor
By Henry D. Spalding
Middle Village, NY: Jonathan David Publishers
1976
Pg. IV:
Hmmm, how does that one go about the crook who got inside the house by climbing intruder window?
   
22 November 1994, Chicago (IL) Tribune, Kidnews, sec. 7, pg. 11, right masthead:
How did the burglar get into the house?
Intruder window.
 
Google Groups: comp.mail.pine
posting single message to number of people, but hiding details.
Stewart Boddy
2/21/97
(...)
“In need of some dough
  A thief got into my house
  Intruder window.”
-Author unknown to me
 
Google Groups: alt.humor.puns
Puns of the Weak: 5-26-00
Stan Kegel
5/27/00
(...)
In need of some dough
A thief got into my house
Intruder window. (Gary Taylor)
     
Twitter   
Mel
@TheDudettAbides
How did he get in, the intruder window?! Bahaha
12:18 AM - 17 Jun 2008
   
Twitter
Austin Nunn
@AustinCNunn
Replying to @PynkPandah
@pynkpandah “There’s an intruder? How did he get in? Intruder window?” I laughed so hard I ended up in coughing fits when I saw it in SS….
2:18 AM - 19 Apr 2009
 
Reddit—Cleanjokes
Posted by u/Mick_Hardwick April 2, 2013
How did the burglar get into the house?
Intruder window
 
Reddit—Dadjokes
Posted by u/Cirrus_Minor July 7, 2019
How do you break into a house?
Intruder window.