And if that is the case run the Convert to Linestring command or right click and select Edit to change it to a linestring. The solution Nick mentions adds nods to the TIN Surface only without creating points or extra nodes in the lines. The default setting for that can be found in Project Settings, Computation Settings, Surfaces, Maximum Sampling Distance - that is applied to all lines included in surfaces - I would set that to a value like 25 or 50 by default or tighyer if you want all your lines subdivided when used in a surface model.
Each line can have an override applied if you want to loosen or tighten up the interval for some reason.
This morning I was also asked about this in a training, if I could apply this to either a selection of lines or to all the lines included in a surface.
1) If you add lines to a surface they are members of that surface. In View Filters - Selection Set - you can select Members of Surface XXXX - then you will only see the lines and points that make up the surface with the surface - turn on all the layers so that all lines of that surface are visible. Turn off the surface to hide it. Now select all of the lines - this only works on linestrings so if you have a mix of Polylines, CAD Lines and Linestrings you will need to select Linestrings only in the pull down at the top of the Properties Pane. Now the setting Override Segment Length property will be visible, and you can make a global change to Yes and then input the sampling interval that you want to use for that surface
2) Applying to a selection of lines is the same approach - select the linestrings that you want to change and then change this property to yes and then change the displayed value to what you need.
Changing the property in Project Settings will apply to all lines in all surfaces automatically. Make sure that you also set the Horizontal and Vertical Tolerance values there as well so that your curved lines and lines that include vertical curves are also densified in the TIN Model