The response comes in two parts....
Part I!
We don't know for sure that Mr Oswald made this denial. We now know that he told Captain Fritz & Company he "went outside to watch the P. parade". There was some documentation on this missing for five-and-a-half decades, but thankfully it came to light on 19 February 2019
---------i.e. Captain Fritz & Company suppressed Mr Oswald's claim as to his whereabouts at the time of the shooting.
Therefore! It is perfectly possible that
a)----------------Mr Oswald confirmed that he had indeed brought curtain rods into the building
b)----------------Captain Fritz, knowing that 2 curtain rods were indeed missing from the Paine garage, and understanding the significance of this, suppressed Mr Oswald's claim.
Part I needs to be dealt with before we look at Part II.
He denied that he brought a package to work on that day and he denied that he had ever had any conversation about curtain rods with the boy named Weesley who drove him to his employment. --Secret Service Agent Thomas Kelley report on one of the Nov 23 interviews of Oswald that he sat in on.
https://www.maryferrell.org/showDoc.html?docId=29105-----------------------------------------------------------------
Mr. FRITZ. And I asked him about that and he denied having anything to do with any curtain rods. It is possible that I could have asked him that on one of those other times, too, but I know I asked him that question the last morning. -- Capt. Will Fritz
http://mcadams.posc.mu.edu/russ/testimony/fritz1.htm--------------------------------------------------------------------
He denied bringing any package to work on the morning of November 22, 1963. He stated that he was not in the process of fixing up his apartment and denied telling Wesley Frazier that the purpose of his visit to Irving , Texas , on the night of November 21, 1963, was to obtain some curtain rods from Mrs. Ruth Paine. -- FBI Agent James Bookhout
https://www.maryferrell.org/showDoc.html?docId=57697&relPageId=108----------------------------------------------------------------------
Mr. BELIN. What was that about curtain rods?
Mr. HOLMES. Asked him if he brought a sack out when he got in the car with this young fellow that hauled him and he said, "Yes."
"What was in the sack?"
"Well, my lunch."
"What size sack did you have?"
He said, "Oh, I don't know what size sack. You don't always get a sack that fits your sandwiches. It might be a big sack."
"Was it a long sack?''
"Well, it could have been"
"What did you do with it?"
"Carried it in my lap."
"You didn't put it over in the back seat?"
"No." He said he wouldn't have done that.
"Well, someone said the fellow that hauled you said you had a long package which you said was curtain rods you were taking to somebody at work and you laid it over on the back seat."
He said, "Well, they was just mistaken. That must have been some other time he picked me up."
That is all he said about it. --US Postal Inspector Harry Holmes
http://mcadams.posc.mu.edu/russ/testimony/holmes1.htm----------------------------------------------------------------------------
Fritz was the head of the DPD Homicide Department. Bookhout, Kelley and Holmes were not under his authority or control. Were all four of those people lying when they stated that Oswald denied the curtain rods?