Is this the standard LCL TTreeview? AFAIK, it has no immediate built-in checkbox support. And in the LCL TTreeView I do not see this issue. I am confused...
Or are you talking of VirtualTreeView? It has a multi-column mode which works with several columns, like in a StringGrid. If you entered this and your node text exceeds the width of the 0-th column, it looks exactly like in your screenshot.
Moreover, your TreeView screenshot shows wrapped node text in two lines. This is also no standard behaviour. You must be using custom-painting. But without seeing your code, nobody can solve your issue.