I'm pretty sure 伝い歩き (つたいあるき) is the correct word and 伝え歩き isn't a standard word. It's like an OCR mistakes or a typo, not 100% sure.
Edit: Yeah, it's 伝え歩き [sK] ("search-only kanji form") on JMdict. I think it's just a very common misspelling?
I can't find it in JP dictionaries and there are a few articles saying it's wrong, so I'm just going to assume it got pulled incorrectly from JMdict. Mind you, JMdict isn't claiming that it's a standard spelling in the first place. They only observed enough occurrences to make it searchable.
Update: I was only able to find native sources speculating about a possible meaning of 伝え歩き, but they ultimately still treat 伝い歩き as the correct word. I couldn't find anything supporting 伝え歩き as an established term with that meaning.
Sources that discuss its meaning generally appear to be trying to rationalise a non-standard spelling rather than documenting actual usage.
A display bug probably. Also, I couldn't find 伝え歩き, it redirect me to 伝い歩き and 伝え歩き was an alternative writing (maybe that's you have that weird bug).
Side note too but 伝え歩き is incorret. 伝え come 伝える and the meaning become something spreading rumors, information while walking. 伝い on the other hand come 伝う and the meaning become walking along someone/something roughly.
EDIT: Definitly a bug, when I typed 伝え歩き, I got this
But when I typed 伝い歩き, I got that
EDIT 2: Not a misspelling. I found a few article explaining the difference in japanese. But probably a mistake with JMdict/jitendex
