  In this paper and a companion one, we study the effect of integrable line
defects on entanglement entropy in massive integrable field theories in 1+1
dimensions. The current paper focuses on topological defects that are purely
transmissive. Using the form factor bootstrap method, we show that topological
defects do not affect the the entanglement entropy in the UV limit and modify
slightly the leading exponential correction in the IR. This conclusion holds
for both unitary and non-unitary field theories. In contrast, non-topological
defects affect the entanglement entropy more significantly both in UV and IR
limit and will be studied in the companion paper.
