TalkTalk said the credit is equivalent to the cost of the connection fee and three months worth of charges for the myTalkTalk Essentials package.
Priced at £6.49 per month, myTalkTalk Essentials offers broadband up to a speed of 8Mbps, a monthly 40GB download limit, free wireless router and a free technical support helpline as well as unlimited phone calls to UK landlines in the evenings and weekends.
TalkTalk hasn't commented on why it's offering the incentive and whether it plans to extend it to other ISP customers.
James Parker, broadband manager at comparison website Moneysupermarket.com, said: "Issuing Tiscali customers with a 'come and get me' offer is a bold move by TalkTalk and Carphone Warehouse. Understandably Tiscali customers may be concerned with the financial situation of their broadband provider, however they should be reassured that there are plenty of good deals on the market so it really pays to look at all the offers available".
"I would urge customers to consider their needs and what they want most from their broadband provider. Customers should look at their usage, how much they download, the speed they want from their service and how much they can afford to pay for it. A deal is only good value if it suits your needs."
See also: Sky drops £450m Tiscali bid