The Bible is a Book of Tales (Narrative Theology)
This blood colored symbol on her house is what the messengers of the Lord use to identify her as holy, and as a symbol of their agreement (covenant) it calls death to pass over her and her family- they are saved.
This reminds us of Jesus’ blood.
It would not have reminded Joshua of Jesus – (same name, different century).
But it would have reminded Joshua of the Exodus Passover:
The Israelites slaughtered substitutionary lambs – redeeming their firstborn from death. The blood went on the doorposts and lintels.
This blood colored symbol on their house is what the messenger of the Lord used to identify them as holy, and as a symbol of their agreement (covenant) it calls death to pass over such a family- they are saved.
This exodus sign is exactly what Jesus places himself in by dying on the passover, and by claiming that the passover blood is his blood. (To read from Luke 20, click the reference, and read both verses on the page – Luke 22.11,20)
That’s just nice.