How to fix my 2001 Chevy Tahoe tow/haul keeps coming on when not pushed. If I leave it unattended will it cause my transmission problems cause I just had to replace it

If you just had trans replaced bring back to shop and have them check their work

Tow/haul mode enables the operator to achieve enhanced shift performance when towing or hauling a load. When tow/haul mode is selected, the tow/haul switch input signal to the body control module (BCM) is momentarily toggled to zero volts. This signals the powertrain control module (PCM) to extend the length of time between upshifts and increase transmission line pressure. Cycling the tow/haul switch again disables tow/haul mode and returns the transmission to a normal shift pattern.

Would't trust it , take an have DTC'S - diagnostic trouble codes checked by a qualified repair shop with a factory or professional scan tool . Auto part stores can not check BCM code's .
DTC B2722

Tow/Haul Switch/Indicator Always On or Inoperative

Step
Action
Value(s)
Yes
No
1
Install a Scan Tool .
Turn ON the ignition, with the engine OFF.
Cycle the tow/haul switch while observing Tow/Haul Mode on the Scan Tool .
Does the Scan Tool display Active when the switch is first pressed, and then Inactive when the switch is pressed again?
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Go to Intermittent Conditions in Engine Controls - 4.3 L or Intermittent Conditions in Engine Controls - 4.8 L, 5.3 L and 6.0 L
Go to Step 2