There were 2 cases which determined whether "pamphleteering" on walkways of privately-owned shopping malls was protected as free speech.
Every time I try to search for them, for some reason, I come up against this NY Times opinion piece from 1986 which explains it succinctly.
Hudgens v. National Labor Relations Board, 424 U.S. 507 (1976) determined that private shopping centers were not subject to Federal First Amendment constraints.
Pruneyard Shopping Ctr. v. Robins, 447 U.S. 74 (1980) determined that states enhancing freedom of speech rights by mandating access to walkways of privately-owned malls did not violate the mall owners' property rights under the Federal Constitution.
The result is that it is squarely up to the state whether this is legal or not. Some states have made it legal and some have not.
This memo, prepared for Connecticut General Assembly, reports that the 5 states which have mandated malls to allow pamphleteering on their walkways are "California, Colorado, Massachusetts, New Jersey, and Washington."
Texas is not one of those states.1 Which puts privately-owned walkways of malls in Texas on par with other privately-owned land. The owners have the same protections on that land as the stores have inside of their premises.
If a store owner can kick you out, then the mall owners can use the same means (whatever they maybe legally) to kick you out of the mall if you do not leave when asked.
1 The CGA report is from 2004. I have not been able to find if any other states have introduced similar enhancements to free speech since then. So the safe assumption is that none have (and, more specifically, Texas hasn't).