you can make your own tea bags by using a square of cheese cloth or muslin folded over a few times, place the loose tea in it, use butcher's twine to tie the bag up and there you go!
you can even untie the twine and re-use the cloth for other bags.
What's good about this hack is that you can make tea bags of any size depending on how large you cut the cloth.
so you can make single serving ones for just a cup or you can make larger ones for when you want an entire pot of tea.
If you don't have cheese cloth/
muslin
I suppose you could use another fabric
but you really want something thin so that the water can seep in and mix with the tea and also to let flavor out of the bag and into the tea.
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To add to the cheesecloth idea...
coffee filters can also be used to make a pouch for a bundle of leaves.
I would caution to be careful of using fabrics or materials that are not food-safe as they may contain chemicals that will leach right into the tea along with the good stuff.
lifehacks.stackexchange.com/users/2781/LivedWithOtters
After looking at a tea strainer on Google something immediately came to my mind, however it will involve perhaps demolishing a sieve.
If you happen to have an old sieve that you are willing to modify somewhat then that's great - carry on reading.
Step one
: Remove the old metal mesh from your old strainer, some wire cutters would work on a stronger metal but scissors may work or you may even be able to push the metal out.
Step two
: Remove the metal mesh from your sieve and cut out a square / circle or whatever of the material the same or a similar size to the piece that you have just removed from the old strainer.
Step three:
Insert newly made mesh into the old casing and seal it down with some glue - leave to dry for a day to make sure that it is fully cured and won't get into your beverage.
Step four
: You should now have a makeshift tea strainer thing - probably won't be as fine a mesh than the original but should suffice for most tea leaves.
Note, if you do not want to use the old casing you can probably makeshift your own out of paper clips or metal wire and shaping them into whatever shape
you want it and then making a cage like thing with the sieve mesh.
Another method I found when looking for a different solution to your problem is to use some tin foil .
I'll summarize the contents of the link I have attached: Cut a foot square of tin foil
Fold in half twice
so it is now a quarter of the original size Pour tea leaves into the center
Bring corners together above the leaves and twist them together making a sort of stick - you'll end up with what looks like a tin foil ball on the end of a tin foil stick When you are ready to brew your tea, poke some small holes in the tin foil ball with a cocktail stick or similar and then brew in the normal way for the normal amount of time!
Here is what it should sort of look like: Good luck.
lifehacks.stackexchange.com/users/2089/MrPhooky
Rather than using a strainer built into your teapot, use an external strainer.
Allow the hot water and loose tea leaves to hang out in your pot, then pour through the strainer into your cup.
This one costs $4 Cdn on amazon.ca.
I'm sure you can find plenty in that price range.
Slightly more expensive ones come with a little bowl to set them down in so as not to dribble on a counter.
lifehacks.stackexchange.com/users/5107/Kate Gregory
Getting a french press for coffee works very well with this.
You don't have to press the leaves down at first if you feel like letting them float for longer.
Then it's up to you when you want to press the leaves down.
It's also extremely easy to clean, and you don't need to make special tea bags or anything that will need to be thrown away after each use.
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My metal mesh tea strainer rusted so I discarded it, but I have failed to find a replacement strainer because this teapot was likely purchased overseas.

In a teapot, how else can I filter the tea leaves steeped in hot water, from the resultant liquid that is poured and sipped? Woefully, this teapot can't be equipeed with a filter at the spout.
How to steep but separate leaves in a teapot without a mesh strainer?
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<food><substitute-tool><kitchen><drinks>
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If you're looking to steep separate leaves without a strainer, you could wrap them in some cheese cloth or muslin. Coffee filters can also be used in a similar way. Alternatively, you could strain the tea by pouring it through an external strainer or even make a makeshift tea-strainer using an old sieve. A French press for coffee also works very well for straining tea. The options are to make your own tea bags out of cloth or coffee filters, replace the strainer in the teapot by cutting out part of an old sieve, buy an external strainer or use a French coffee press.
Make your own tea bags out of muslin or cheese cloth. The can be re-used. Use coffee filters to make bags for the tea. Cut a section out of an old sieve and fit into the teapot where the old strainer was. Buy an external strainer. Get a French press for coffee.