Is there a tool that will let me check which backlinks a site got between a specific time period?
All the tools I've seen like OpenSiteExplorer just show all the backlinks.
A tool that lets you see them on a timeline would be really helpful to see which of your marketing efforts worked at that time.
ahrefs is a tool that comes closest to what you're looking for; it has a 'new backlinks' report that shows over a multi-month period which days they found new backlinks for a given URL.
A caveat with any tool is going to be that it can only show you backlinks based on when it detected them (all of these tools operate by crawling the web and regularly re-crawling it, just like Google). ahrefs shows a "placed between" window of time that is presumably the dates when it discovered the link and when it last checked that site.