Jos 2:3 And the king of Jericho sent unto Rahab, saying, Bring forth the men that are come to thee, which are entered into thine house: for they be come to search out all the country.
We are not told what made the spies conspicuous. However, we know the following facts: (1) Jericho and the surrounding cities were aware of the approach of the Hebrews and the start of their campaign, (2) their deportment, dress and accent may have contributed as well. The fact that they entered a prostitutes house and did not defile themselves by lewd talk may have been noticed. We are not told.
Verse 2 states that "someone/sombody had said that to him". The hebrew text use וַיֵּאָמַר. We can't find any verse here that say that the spies weren't seen by anyone while entering Rahab's "hotel" (the word חרש here is part of the order by Joshua, not the way they did it).
So even if it was in the middle of the night - someone could (and according to verse 2 actually did) see them coming. And he/she the one that told the king.
Mortals/anshi are half-gods/half-man (adm) - masterful Men (gbrim) of stature.
Gen. 6:4 - The-ones-distinguished (e~nphlim 5303) they-became (eiu 1961) in~(the)~earth (b~artz 776) in~(the)~days (b~imim 3117) the~those (e~em 1992) and~moreover (u~gm 1571) after (achri 310)(-) so (kn 3651) which (ashr 834) they-are-coming (ibau 935) sons-of (bni 1121) the~Elohim (e~aleim 430) to (al 413)(-) daughters-of (bnuth 1323) the~human (e~adm 120) and~they-(gave)-birth (u~ildu 3205) for (l~em 9999) they (eme 1992) the~masterful-(men) (e~gbrim 1368) who (ashr 834) from~eon (m~oulm 5769) mortals-of (anshi 582) the~name (e~shm 8034):p
Josh. 2:1 - Joshua sent two mortals to spy out Jericho. Likely noticeable, even at night.
Josh. 2:2 - And~he-is-being-said (u~iamr) to~king-of (l~mlk) to-say-of (l~amr) behold~! (ene) mortals (anshim) they-entered (bau) here (ene) the~night (e~lile) from~sons-of (m~bni) Israel (ishral) to~delve-of/search-out (l~chphr 2658) ath(-) the~land (e~artz):
Even the king's men didn't accuse the Israelite mortals of entering Rahab's for lewdness. And the king agreed with the assessment of his men.
In Josh. 2:4 and 2:6, Rahab secludes the mortals and let's them know that she is aware of their cause. Rahab is in awe of them. One commentary suggested that Yahweh knew Rahab's heart and sent them directly to Rahab's.
I see absolutely nothing in these verses that suggest the mortals defiled themselves.
Edit: Verses are from Scripture4all.org - ISA2 program.