This problem is almost certainly caused by the thermocouple being used touching something which is at a different potential to the TC-08/PC earth. If this voltage is greater than about +/-7V the channel is pulled out of he common mode range of the TC-08. This causes all channels to read very incorrect values. You must ensure that the metal object you are touching with the exposed end of the thermocouple is earthed correctly and at the same potential as the PC earth. If that cannot be done, the thermocouple must be electrically isolated from the metal surface. Failing that, for short term logging, you can use a laptop running on batteries, that is not connected to mains earth.
The overload can be on one channel, or between channels. The TC08 has an input range of approx 70mV. If more than 5V difference occurs between any of the inputs to the TC08 then incorrect readings will result. Additionally if more than 5V difference occurs between the TC08s ground (also computer ground and usually mains earth) then errors will occur. A typical example where this may occur would be if a thermocouple is used to measure the temperature of the motor on a machine tool. The casing of the motor, although earthed may be at a potential several volts different to that of the earth of the computer.
Plug in the thermocouples one by one to locate which are causing the problems. If possible electrically isolate the thermocouple. If this is not possible, run a wire from the metal outer shell of the TC-08 USB connector to a point near the thermocouple tip. This will earth the area near the thermocouple tip and is often enough to 'pull' the two grounds close enough for normal operation.
Laptops running on mains adaptors can also cause problems. Some laptop power supplies do not have an earth connection and produce large amounts of interference which can be picked up by the sensitive TC08. If you have problems when the laptop is run off it mains adaptor, but not on battery, try earthing the laptop. There is often a screw on the back of the laptop that can be used for this purpose. Alternatively run a wire from the TC08 USB connector shell to mains earth.
Please also see this page about thermocouples-https://www.picotech.com/library/application-note/thermocouple-application-note
The low half of the page lists precautions when using thermocouples.