It looks like there are several versions of the 'threatening letter' sent to Qutuz. The version from the wiki about Qutuz has the following phrasing:
Let al-Malik al-Muzaffar Qutuz, who is of the race of Mamluks who
fled before our swords into this country, who enjoyed its comforts and
then killed its rulers, let al-Malik al-Muzzafar Qutuz know, as ...
(I saw your other question on Qutuz's mud-slinging with Hulagu. So, I hope I don't blow your bubble here).
What did the Golden Horde get out of the alliance with Mamluks?
Answer: They did not have one. The Mamluks claimed they had an alliance with the Golden Horde, but that's just it: a claim and a very long con by the Mamluks. Gives new (old?)...
Yeah Golden Horde had some benefit from this allies with the Mamluks
Money from every slave sold to Mamluks
With Hulegu fight on two front with Mamluks and Berke so Hulegu cant form full scale coordinate attack to golden horde with chaghatayid from central Asia
Berke can deter chaghatayid with this action against Hulegu... golden horde greatest enemy was ...