RE:RE:RE:Hmm...Think of rights like a contract that one can opt into, with a 30 day expiry, and these contracts are given out as a dividend.
Rights were given to shareholders of record on May 25, and the stock went ex-rights (meaning, no attached "dividend" if you buy on or after this date) on May 22. These Rights will appear as separate securities in your account, under ticker TEK.RT, hopefully tomorrow.
If you so choose, you can "exercise your rights", which involves calling your broker and telling them you would like to exercise your rights. So, if you have 1000 shares, you will have 1000 TEK.RT rights. The exercise price is 1.5 cents per unit, so you will have to forward to your broker, at the end of the rights offering, .015*1000 = $15, to receive 100 units. Each unit consists of 1 share and 1 warrant. So after all is done (assuming you didn't sell your initial shares), you would have 1000 new tekmodo shares, 1000 warrants, and 1000 of your initial shares.
So, to answer your question, you can only exercise your rights within the given 30 day window, expiry being June 26th I think. After that point, the rights in your account become completely worthless. If you don't plan on exercising your rights, it would be worth it to sell those rights on the open market. I would guess that they are going to sell for at least 1 cent (given that TEK stock is trading for 3 cents currently).
Hope this helps