I like to wash out modifiers (acid or base) from my columns before storing the columns (or the end of the day if I'm leaving the column on the system) as they last longer.
Remember that TEA is basic. If the pH is below 7.5, it will be ok. If above 7.5, the mobile phase will start dissolving the silica underlying the C18 and this will reduce column life.
Without knowing what the pH and any other components of your mobile phase are it is difficult to provide a real answer.
Jack is correct in his statement that if the pH is below the upper pH limit of the column (which can vary from 7 to 12 depending on the type of C18 column) you will be okay. However, unlike Jack, I prefer not to wash out modifiers unless the column is going to be stored for a long period of time. If you are constantly using the system I find it advantageous to just lower the flow to a small amount (ie. 0.1mL/min on systems that normally run 1.0mL/min). That way it reaches a steady operating state much more quickly for the day's runs.
because TEA was used to decreased interaction between basic ( amine) coumpounds and residual silanols, after 1 liter of mobile phase you modify the column phase : the phase is C18+ TEA.
( please remember than silica "love" amine compounds : if you work on proteins, you never used glass vessels.)
if you want to test some others conditions without TEA, please use a new column!